Image source, Reuters

Donald Trump gave a press conference after it became clear that talks with North Korea had ended two hours early, and without a peace declaration being agreed.

Here are the key bits:

• He said there were options for a deal but "we decided not to do any of the options", adding: "It wasn't a good thing to be signing anything."
• Secretary of State Mike Pompeo said both sides had resolved to continue and he was still optimistic.
• However, there is no firm commitment to a third summit.
• In the end, it was about the sanctions - North Korea wanted them lifted entirely in exchange for dismantling its Yongbyon nuclear facility. The US wasn't willing to agree to that.
• But Trump said Mr Kim promised him he would continue not test nuclear weapons or long-range missiles.
• Trump said he has a "great relationship" with South Korea's President Moon Jae-in and would call him soon to discuss the outcome.
• He condemned the fact his former lawyer and fixer Michael Cohen gave testimony to Congress during the summit, calling it "terrible" and branding Cohen a liar.
• Trump said he believed Mr Kim did not know about the alleged torture of Otto Warmbier, an American student who was detained in North Korea and died days after he was returned to the US in July 2017.

Laura Bicker
Seoul Correspondent

The lack of progress or plan to get Kim Jong-un to give up his weapons will allow critics to ask what is the point.

Many claim Donald Trump is giving Mr Kim a global platform to appear to be a normal, peace-loving nuclear power. However, those close to these negotiations say they are laying the groundwork for a relationship with North Korea. Now Mr Kim has his arsenal, these talks will at the very least ensure he is unlikely to use it.

Hanoi has heavily branded itself as the "City for Peace" this week - these signs are everywhere.

A summit which is being reported around the world as a failure is going to be hugely disappointing. The authorities here clearly wanted Hanoi to be known as the location which witnessed a breakthrough, not a collapse.

Donald Trump has now ended the media conference at the Marriott Hotel.

"I'm about to get back on a plane and fly back to a wonderful place called Washington DC," he said.

The entire press conference lasted about 40 minutes.

Image source, Reuters

Mr Trump was asked whether he wanted to apply even more sanctions on North Korea.

"I don't want to talk about increasing sanctions. They are strong," he said.

"There are people in North Korea that have to live also... I would say my whole attitude changed a lot because I got to know Chairman Kim very well."

Earlier he said that North Korea wanted all sanctions lifted but "we couldn't do that".

Image source, AFP

Mr Trump is very clearly insisting that Mr Kim knew nothing about the case of Otto Warmbier, the US student who was jailed in North Korea and died shortly after being sent home on medical grounds.

Mr Warmbier's parents believe he was tortured and killed by North Korea. Ahead of this summit, there were appeals to Mr Trump to raise it with Mr Kim., external

He says he did and that Mr Kim felt "bad" about it, but was not involved in Mr Warmbier's treatment or death. Here's what we do know about what happened to Otto, who went to North Korea on an adventurous holiday.

Image source, Reuters

Mr Trump confirms that he and Mr Kim have discussed American Otto Warmbier, who was detained in North Korea and died days after he was returned to the US in July 2017.

"We've talked about it... I really don't think it was in his interests at all. I know the Warmbier family very well. I think they’re an incredible family. What happened is horrible. I really believe something very bad happened to him, and I don't think the top leadership knew about it," Mr Trump says.

"[...] I got the prisoners back, I got the hostages back... Otto came back in shape that was not even to be talked about. The others came back extremely healthy...

"I did speak about it, and I don't believe that he would have allowed that to happen. It just wasn’t to his advantage to allow that to happen. Prisons are rough, they're rough places, and bad things happened."

He says Mr Kim "felt very badly about it", adding: "He knew the case very well, but he knew it later. [...] In those prisons, those camps, you have a lot of people.

"He tells me he didn't know about it, and I will take him at his word."

"We'll be able to do that very easily," said Mr Trump when asked about international inspections of North Korea's nuclear sites.

But he did not suggest this would happen anytime soon.

"The inspections on North Korea will take place... if we do something with them. We know things about certain sites and certain places... we would be able to do inspections very successfully."

Mr Trump has been asked by NK News what he will say to South Korea's President Moon Jae-in.

Mr Moon can only serve one term in office, and he's nearly done. It's been something of a personal mission for him to achieve a breakthrough with North Korea, and he has had his own landmark meetings with Kim Jong-un. South Korea has a lot to lose if North Korea walks away from diplomacy entirely now. Which it has done before.

"I like President Moon very much... we have a great relationship," said Mr Trump. "Believe it or not I have a great relationship with almost every leader but some take advantage of our country.

"We'll be calling Moon very soon and he'll be one of the first calls, I'll be calling Abe of Japan [too]. Moon is working very hard - he'd love to see a deal, he's been very helpful."

Image source, Reuters

There is no commitment between both leaders so far to hold a third summit.

Mr Trump added that "a second uranium enrichment plant" came up during talks, saying that North Korea was "surprised" at what the US knew.

Experts say that aside from Yongbyon, North Korea has at least two other undeclared sites where uranium can be enriched.

Mr Trump believed that diplomacy had been done the wrong way with North Korea. He made a great deal of how his negotiating skills could achieve a breakthrough no-one else had. Sokeel Park in Seoul will not be the only person pointing out there will be some schadenfreude going on today.

Mr Kim was willing to dismantle North Korea's Yongbyon facility but wanted "all the sanctions" lifted in exchange, Mr Trump says.

He said he wasn't willing to do this.

The BBC's Jon Sopel is at the press conference. He just asked Mr Trump whether it had been premature to meet Mr Kim so soon.

Mr Trump said there had been the potential to have signed something today - "we had the papers ready to be signed" - but it just wasn't "appropriate".

It's been clear that North Korea and the US have different understandings of what "decnuclearisation" means.

For Mr Kim, analysts say, the term refers to the denuclearisation of the entire Korean peninsula - meaning the removal of US troops, who protect South Korea under Washington's nuclear umbrella.

But Mr Trump said he was clear what the term refers to.

"A lot of people don't know what it means but to me it is pretty obvious. They have to get rid of nukes."

This is the scene around the press centre now, as the world's media report Mr Trump's explanation for the lack of a much-heralded breakthrough with North Korea. Maybe he's envying Mr Kim for not having to do the same?

The US president is vague about exactly how the summit broke down.

"I don't want to say it was my decision... I want to keep the relationship - we'll see what happens over the next period of time."

He said he believes Mr Kim will stick to promise of not testing further nuclear weapons or missiles.

"I trust him and I take him at his word - I hope that's true."

It was "terrible" for Michael Cohen's hearing to have taken place during the Hanoi summit says Mr Trump.

"Having a fake hearing like that and having it in the middle of this summit is really a terrible thing. They could have made it next week."