We can bring you more detail now on how the Israeli military is responding to Hamas' statement.

A reporter for Israel's official military radio station, Galatz, has posted that the Israeli military will reduce its troops activity in Gaza "to a minimum".

"After Trump's announcement - the political echelon instructed the IDF to stop the operation to occupy Gaza," reporter Doron Kadosh wrote on X.

Writing in Hebrew, he adds that the military has been instructed to carry out only defensive operations.

Israel's top military chief held an overnight meeting with top officials from the military and intelligence services, according to a new statement from the IDF.

Israel's chief of general staff "convened a special situation assessment in light of recent developments", which also included officials from the Hostage and Missing Persons Headquarters, the statement says.

It adds that at the direction of government politicians, the top general "instructed to advance readiness for the implementation of the first phase of the Trump plan".

The statement goes on to say that the safety of Israeli troops remains a "top priority", and that "all IDF capabilities will be allocated to the Southern Command", which oversees Gaza operations.

The statement does not make mention of specific plans to reduce military activity in Gaza, but calls on troops to be prepared to fight again if needed.

"The Chief of Staff noted that, given the operation sensitivity, all troops must maintain high alertness and vigilance, in addition to reinforcing the need for a rapid response to neutralize any threat."

Moshe Lavi, the brother-in-law of a hostage being held by Hamas, has spoken with the BBC about the deal and stressed the need to immediately see all hostages released.

He says Hamas are the culprits that need to be held to account and forced to accept the plan.

“There shouldn’t be a deal in the first place because the hostages should be released immediately and unconditionally, but we are realistic and understand there is a deal,” he says.

His brother-in-law Omri Miran, was kidnapped and taken to Gaza, leaving his wife and their two daughters behind at Kibbutz Nahal Oz.

Lavi says he now sees hope "that the war needs to end and that the hostages must be released and prioritised".

“No buts and no delays".

A moment ago we saw Israeli PM Netanyahu pledge to implement the "first phase of Trump's plan for the immediate release of all hostages". So what does that mean?

Trump's plan is divided into 20 points, making it unclear what Netanyahu was referring specifically to when it comes to what he called "the first phase".

Plus, the details of Trump's plan are still being finalised, the president said in a video from the Oval Office an hour ago.

According to the 20-point Trump plan:

• Trump's plan calls for Gaza to become a "deradicalised terror-free zone that does not pose a threat to its neighbours"
• It says Gaza "will be redeveloped for the benefit of the people of Gaza"
• After these two steps are reached "the war will immediately end", Trump's third step says. Israeli troops will "withdraw to an agreed upon line" and all hostilities will be ceased
• The two sides will prepare for a prisoner exchange: After Hamas frees all Israeli hostages, alive and dead, Israel will release nearly 2,000 Palestinian prisoners

A social media post by Trump earlier today referred to the third step of his own plan, where he wrote: “Israel must immediately stop the bombing of Gaza, so that we can get the Hostages out safely and quickly!"

Hamas, meanwhile, has said it will release all remaining hostages, but still wants further negotiations to continue.

Read Trump's 20-point Gaza peace plan in full

Image source, Reuters

UK Prime Minister Keir Starmer pledged UK backing for further negotiations and work toward a sustainable peace for Israelis and Palestinians.

He says Hamas' acceptance of at least parts of the peace plan present an opportunity to end the fighing, bring hostages home and for humantiarian aid "to reach those who so desperately need it".

"We call on all sides to implement the agreement without delay."

Image source, Getty Images

Israeli Prime Minister Benjamin Netanyahu's office has just released a two-line statement, saying the country will work with the US on "Trump's plan" for peace.

"In light of Hamas's response, Israel is preparing to immediately implement the first phase of Trump's plan for the immediate release of all hostages," Netanyahu said in a statement translated from Hebrew.

"We will continue to work in full cooperation with the President and his team to end the war in accordance with the principles set forth by Israel that are consistent with President Trump's vision."

• Hamas agrees to release hostages: Hamas says it accepts parts of the US peace plan to end the war in Gaza, ahead of a Sunday deadline US President Donald Trump had set for their response. In its statement, Hamas says it will release all remaining Israeli hostages, but wants further negotiations on the proposal
• Trump's response: Trump welcomed Hamas' response, and urged Israel to stop bombing Gaza, saying he believes Hamas is "‘ready for a lasting peace". In a video recorded in the Oval Office, he thanks a series of countries he says helped broker the plan, including Qatar, Egypt and Saudi Arabia
• Talks to resume: Qatar also welcomed Hamas' statement, and says it is coordinating with Egypt and the US to resume talks about implementing a ceasefire
• Analysis: The developments provide hope for resolution, says the BBC’s John Sudworth, reporting from Jerusalem, but he cautions many details still need to be worked out. BBC State Department correspondent Tom Bateman says that those details are crucial to the whole plan’s implementation

Anthony Zurcher
North America correspondent

It wasn’t a long video message, but Donald Trump got his point across. Calling it a “big day” and a “very special day”, the president made a particular effort to thank the Muslim nations that had worked with the US to broker a deal that Hamas could – at least partially – accept.

While Trump acknowledged that the “final word” has not been given, if his efforts have succeeded in convincing Hamas to release all the remaining hostages, living and dead, he will have notched a significant diplomatic victory - one that his administration, and Joe Biden's before it, had laboured hard to secure.

Interestingly, Trump made no mention of Israel in his message, even though pressuring Prime Minister Benjamin Netanyahu to sign off on the American peace plan was one of Trump’s more noteworthy accomplishments during these fraught negotiations.

No one in the White House will be popping champagne corks just yet, but the president is clearly optimistic – and grateful.

Momentum behind peace talks gains more steampublished at 00:07 BST 4 October

00:07 BST 4 October

Lyse Doucet
Chief international correspondent

No one wants to be seen to say “no” to US President Trump right now – not even Hamas.

Their carefully crafted statement, issued under huge pressure and no doubt input from mediators including Qatar, Egypt, and Turkey, was a “yes” – albeit a very incomplete and conditional one.

It only highlights a few issues which matter most, including giving up all the hostages, living and dead, ending the war, and accepting that Gaza will be governed by technocrats.

They also made a point of thanking Trump, along with “the Arab, Islamic, and international efforts".

Hamas’s statement also sidestepped the issues in Trump’s 20-point peace plan which they still reject including the demand to give up their guns.

Their gamble succeeded, at least for now, with a US President who is more focused than ever before on ending this war, who wants to be seen as a winner; he immediately latched onto Hamas’s reply as proof that peace is possible.

Once the Israeli sabbath ends tomorrow, Israel’s Prime Minister Netanyahu seems certain to be more sceptical.

But the new momentum behind ending Gaza's grievous war, which gathered pace last week, has just gained a bit more steam.

Trump has released just a video message on social media in response to Hamas' statement.

He thanks Qatar, Turkey, Saudi Arabia, Jordan and Egypt for their efforts in helping him negotiate a peace deal.

"This is a big day, we'll see how it all turns out. We have to get the final word down and concrete," he says, adding that he looks forward to "having the hostages come home to their parents".

"We're very close to achieving" peace in the Middle East, Trump says.

All eyes now on Netanyahupublished at 23:46 BST 3 October

23:46 BST 3 October

Bernd Debusmann Jr
Reporting from the White House

Trump's response to Hamas and his demand for Israel to stop bombing Gaza comes amid what some observers have described as an increasingly awkward relationship between the president and Israel.

On one hand, Trump has portrayed himself as a staunch defender of Israel - and Prime Minister Benjamin Netanyahu is quick to describe him as his country's "best friend".

On the other hand, Trump has reportedly grown increasingly frustrated with Netanyahu's government and its conduct. In June, he famously used an expletive to describe continued fighting between Israel and Iran when an end to their conflict was within grasp.

More recently, he expressed disappointment when Israel bombed Qatar, a key US ally that hosts an enormously important US airbase.

All eyes are now on Netanyahu, who is facing enormous domestic pressures, including from some in his own coalition who want to end the war militarily.

If Israel hesitates in agreeing to come to the table despite Hamas' only partial acceptance of Trump's 20-point plan, many in the US and the Middle East will be looking to see how forcefully Trump is willing to criticise Netanyahu.

A Hamas spokesperson tells the BBC that US President Trump's comments are "encouraging".

The spokesperson says the group is "ready to begin negotiations immediately to achieve a prisoner exchange, end the war, and secure the withdrawal of the occupation".

We're now hearing from Qatar, which has been pivotal in negotiations to end the war in Gaza.

It says it welcomes Hamas' statement, adding: "We also affirm our support for the statements made by the President calling for an immediate ceasefire to facilitate the safe and swift release of hostages, and to achieve rapid results that would put an end to the bloodshed of Palestinians in the Gaza Strip."

It also says that it has begun coordinating with mediator Egypt and the US to resume talks about implementing a ceasefire.

Trump wants peace deal over the line - but we're still not there yetpublished at 23:12 BST 3 October

23:12 BST 3 October

Tom Bateman
US State Department correspondent

Image source, PA Media

Trump always wanted one thing the most: to be able to stand up and say he has got all the hostages out and ended the war.

Hamas’ statement, in his view, gets to the verge of that moment. He’s framing it as Hamas signalling that it wants “lasting peace”.

Then we have the extraordinary line, given that it comes from the president of the US, that Israel “must immediately stop the bombing of Gaza” so that the hostages can be released quickly.

There is only a nod to how this will all be implemented: “We are already in discussions on details to be worked out”.

But the details to be worked out remain crucial for the whole plan’s implementation. Hamas handing over all the living hostages means they lose nearly all their bargaining power, and that becomes important given what they’re saying in the final part of their statement - appearing to reject Trump’s call for their disarmament and exile as part of the package to end the war.

They also want a complete Israeli withdrawal from Gaza. We are at an absolutely critical moment and Trump wants it over the line immediately - but we’re still not there yet.

A lot of detail to be worked out before peace can become realitypublished at 22:49 BST 3 October

22:49 BST 3 October

John Sudworth
Reporting from Jerusalem

Hamas agreeing to release the remaining hostages, albeit subject to negotiations and certain conditions being met, will give real hope to the family members here in Israel who have been desperate for this kind of news for a long time.

And the acceptance of another key part of the peace plan, the idea of handing over the governance of Gaza to Palestinian technocrats is also clearly significant. But there are plenty of other elements that are glaring by their absence, most notably the requirement that Hamas lay down its arms.

The Israeli government will now be poring over the wording to glean the true intent, and to decide whether it sees this as a genuine good faith acceptance of some of the key points of the deal or merely an attempt to buy time and reopen long drawn out negotiations.

Given that it came just a few hours after Donald Trump issued his final ultimatum for Hamas to agree or face "all hell", some members of Israeli Prime Minister Benjamin Netanyahu's cabinet are likely to be sceptical, particularly now the US president has called on them to immediately stop the bombing of Gaza.

They also won't like the last paragraph suggesting Hamas would retain a role in negotiations over the long term future of Gaza. The statement is significant no doubt, but there's still a lot of detail to be worked through before peace becomes anything like a reality.

Trump appears to get what he most wanted from the dealpublished at 22:40 BST 3 October

22:40 BST 3 October

Bernd Debusmann Jr
Reporting from the White House

I left the White House this afternoon just as news of Hamas' partial acceptance of the peace proposal was breaking - and with no clear indication of how Trump would respond.

My quick initial inquiries were met with stony silence. Now, we have Trump's response, in which he says he believes Hamas is "ready for a lasting peace" and that "Israel must immediately stop the bombing of Gaza" to allow the hostages to be freed.

For months, I've been in briefings, Oval Office meetings and trips with Trump in which he made his one primary demand very clear: that the hostages be released before any further progress was possible.

A failure to do so, the White House said as recently as this afternoon, would create a situation in which Trump gives the Israeli government free reign to accomplish its remaining military aims.

Even with many details left to be worked out, Trump appears to have gotten the response he wanted.

Timings remain unclear. But as things stand, it appears that Trump has now put the onus on Israel to stop its operations in Gaza.

We're going to hear more from Trump later today, and likely over the weekend if there appears to be progress - or complications - in the negotiations.

In its statement responding to the US peace proposal, Hamas says it agrees to "release all Israeli prisoners, both living and dead, according to the exchange formula contained in President Trump's proposal, provided the field conditions for the exchange are met".

It adds that it "renews its agreement to hand over the administration of the Gaza Strip to a Palestinian body of independents" based on "Palestinian national consensus and Arab and Islamic support".

On the future of Gaza and rights of the Palestinian people, Hamas says this is "linked to a comprehensive national position based on relevant international laws and resolutions, and are being discussed within a national framework" of which it will be a part.

Tom Bateman
US State Department correspondent

Trump has run out of patience with ending this conflict and is eager to see some type of results.

It's unlikely that Trump will let this back-and-forth over terms to go on for months, and might rely on countries like Qatar and Egypt to help negotiate.

This is likely to be an intense negotiation.

Trump has just released this statement on his social media platform, Truth Social.

It says: "Based on the Statement just issued by Hamas, I believe they are ready for a lasting PEACE. Israel must immediately stop the bombing of Gaza, so that we can get the Hostages out safely and quickly!

"Right now, it’s far too dangerous to do that. We are already in discussions on details to be worked out. This is not about Gaza alone, this is about long sought PEACE in the Middle East."

President Trump is recording a video message to respond to Hamas' statement on his proposed peace plan.

White House Press Secretary Karoline Leavitt has shared a photo of the president behind the Resolute Desk as he records a message in front on a camera.

Image source, X/White House Press Secretary