Deaths in the US - the country with by far the world's highest toll - near 100,000
President Trump has come under fire for playing down the pandemic in its early stages and giving dangerous and misleading advice
But the White House says he saved many lives by making the "very hard choice" to shut down the economy
In the UK, the official death toll of confirmed coronavirus cases rises by 134 to a total of 37,048
Health Secretary Matt Hancock says the UK may review fines given to families who breached lockdown to get childcare
It comes after a UK junior minister quit over the actions of top aide Dominic Cummings, who is accused of breaking the rules
Denmark is easing controls with other Nordic countries, allowing cross-border couples to meet again
Germany plans to end its travel warning for trips to 31 European countries from 15 June
Globally, the number of infections has passed 5.5 million and more than 346,000 people have died - Johns Hopkins University
Running through the daily slides, Prof John Newton, the national co-ordinator of the UK's Covid-19 testing programme, says there's a small trend upwards in motor vehicles.
He says that's what we'd expect given the advice about some returning to work.
But he says there's "really no increase" in the use of public transport recently.
Hancock says that today he is announcing a new trial for selective NHS patients of an antiviral drug - Remdesivir.
There have already been some promising results, he says, and it can shorten recovery time.
"This is probably the biggest step forward in the treatment of coronavirus" since the crisis began, he says.
Read more about the antiviral drug here
He says there are two areas he'd like to talk about: Personal Protective Equipment and treatments.
He says they have been "working hard" on PPE provision amid a "global scramble" to acquire it.
He says there has been a "mammoth effort" and they have "ramped up" production of two billion items of PPE here in the UK.
And there are contracts for a further 3.7bn gloves.
"These new supplies mean we are not simply keeping up with demand, we are able to begin to replenish our stockpiles."
The UK's Health Secretary Matt Hancock begins by saying that for the first time since 18 March, there have been no deaths recorded in Northern Ireland.
And he says the ONS statistics show the overall number of deaths are the lowest in six weeks.
"The number of deaths is falling," he says. "We must keep our resolve."
The UK's Health Secretary Matt Hancock has begun his opening remarks at the daily Downing Street coronavirus briefing.
We'll bring you the latest from that briefing here.
The UK's daily briefing will start in a few minutes. Stay with us for all the crucial updates.
At yesterday's briefing, Boris Johnson announced that non-essential shops in England will be able to open from 15 June. So while we wait for today's briefing, why not have a look at this video on how to shop safely?
Coronavirus: How to keep safe while shopping
Image source, AFPThe UK government briefing is due to start in 15 minutes.
Health Secretary Matt Hancock is likely to face questions about whether the prime minister's most senior adviser, Dominic Cummings, broke lockdown rules when he drove from London to Durham with his sick wife.
The story generated a political storm over the weekend, and this morning a junior minister resigned from the government. Thirty Conservative MPs have called on Mr Cummings to resign or be fired.
Find out everything you need to know with our round-up here.
Merck, one of the largest vaccine makers in the world, is jumping into the race to find a coronavirus vaccine.
The US company announced on Tuesday that it was pursuing two paths towards a vaccine.
Merck is buying Austrian company Themis Bioscience, which is currently tweaking an existing measles vaccine for possible Covid-19 use. Clinical trials are expected to begin in weeks.
The second track is a partnership with research firm IAVI, which is adapting Merck's Ebola vaccine.
It comes after President Trump announced "Operation Warp Speed" with promises of a vaccine “by the end of the year or shortly thereafter”.
But on Tuesday, Merck CEO Ken Frazier cast doubts on the US government's 12 to 18-month timespan.
“It is not something I would put out there that I would want to hold Merck to,” he told the Financial Times, warning that "very large" clinicals trials would take months or even years to complete.
Meanwhile, US-based biotechnology firm Novavax has announced that human trials for a possible coronavirus vaccine have begun in Australia.
The trial includes 131 volunteers from Melbourne and Brisbane, the company says.
The daily UK press briefing is due in half an hour. We'll be bringing you all the updates from Health Secretary Matt Hancock.
In the meantime, here's a look at what's happening in the UK this afternoon:
Image source, EPASpain is going to hold a 10-day mourning period from Wednesday, government spokeswoman Maria Jesus Montero has said.
She told the government briefing that flags on all official buildings and military ships will fly at half mast, in memory of the people who've died of coronavirus in the country.
At the end of the 10 days, a memorial ceremony will be held.
"They are not with us anymore physically, but they will remain forever in our memories and we will honour their memories as they deserve it, with an official and great act of tribute which will be led by the head of state," Ms Montero added.
A total of 26,834 people have died of the virus in Spain, according to the count kept by US-based Johns Hopkins University.
We have just had it confirmed that the UK government will give its daily briefing at 17:00 BST (16:00 GMT).
The briefing will be led by Health Secretary Matt Hancock.
He will be joined by Prof John Newton, the national co-ordinator of the UK's Covid-19 testing programme.
Katy Watson
BBC South America correspondent
Image source, AFPFederal police in Brazil have raided the residences of Rio de Janeiro’s governor Wilson Witzel as part of a corruption probe over Covid-19.
According to a statement by the Federal Police, the search warrants were issued over the involvement of public money used to fight the virus in the state of Rio de Janeiro.
It said evidence pointed to alleged irregularities regarding field hospitals set up to help treat patients with Covid-19. In total, 12 search and seizure warrants were issued. No arrests have been made.
In a statement, Witzel said that he was innocent, and accused the president of interference. Jair Bolsonaro, for his part, congratulated the Federal Police for the move.
Image source, Getty ImagesA retired chemistry teacher who spotted Dominic Cummings in County Durham says he has some regrets over getting involved.
Robin Lees told BBC Radio Newcastle it had been a “difficult few days” after his account of the encounter with Mr Cummings was initially brushed off by Downing Street, but felt “vindicated” by Mr Cummings' subsequent admission.
Mr Lees said: "When I gave my name I didn't expect... it to be quite like it occurred."
He said he recognised Mr Cummings after seeing him in the press. "I just know what he looks like and this person looked strikingly like him," he said.
Crucially, Mr Lees remembered the number plate of a car used by Mr Cummings, wrote it down, and searched the number online.
"At the time I just put it out of my mind," he said, before reading the first reports on Friday evening and emailing a Guardian journalist. The story has dominated UK politics ever since.
It's been almost one week since all 50 US states began to reopen, but some are going more slowly than others.
Georgia, one of the states to reopen earliest, has seen a steady stream of around 600 new cases daily but has not reported any spike.
Michigan, which saw its stay-at-home order extended before the Memorial Day weekend by the governor until 12 June, is starting to ease restrictions in the least affected parts of the state as well as in Detroit.
Starting Tuesday, Michigan's retail and auto businesses can reopen but with limited customers. Bars and restaurants have already reopened in the more isolated parts of the mid-western state.
In New Jersey, where gyms, hair salons and other close contact businesses are still closed, a group of around 500 business owners say they will flout the rules and reopen on 1 June.
Senior bishops who criticised Dominic Cummings' lockdown travel say they have received death threats.
Bishops in Newcastle, Ripon and Liverpool are among those who have said they have received hate mail.
A number of church leaders criticised Mr Cummings' trip from London to Durham to self-isolate.
Bishop of Worcester John Inge said he got a "delightful email" saying: "Stay out of politics or we'll kill you."
Read more here.
Following on from Samira Hussain's piece a few moments ago, it has now happened....
New York Governor Andrew Cuomo has rung in the start of the trading day at the New York Stock Exchange, marking its return after a two-month closure.
“In the two months the floor was dark, NYers bent the curve and slowed the spread of this virus,” the governor tweeted.
Under new measures at the NYSE, only a quarter of the normal number of traders will be allowed to return to work.
Traders must also avoid public transport, wear masks and follow strict social distancing rules, with newly fitted transparent barriers to keep people apart.
New York City has been hit hard by the coronavirus pandemic, with some 200,000 cases and more than 20,000 deaths.
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Faisal Islam
BBC Economics Editor
Image source, Getty ImagesFor Dominic Cummings, the PM's chief adviser, to claim, in the middle of his defence on Monday, "only last year I wrote explicitly about the danger of coronaviruses" is worthy of some inspection.
Such prescience would indeed have been impressive and helpful, and he does have a long-standing and well-known interest in mathematical modelling and big data.
Looking at his blog, there is one reference to coronavirus, and it was indeed in a blog written in March last year. But it wasn't quite as billed. It is a blog about the risk of a pandemic starting from a leak from a biological lab.
The internet archive Wayback Machine, which tracks the changing versions of publicly available websites, shows that the blog was edited some time between 9 April and 3 May this year (after the pandemic started) to insert the reference to coronavirus and Chinese labs.
It is a mystery why he felt the need to burnish his credentials as a coronavirus sage so much that he pointed to having explicitly warned about something that was only added to his blog after the event.
Image source, EPAMink farms have been shut down in the Netherlands
The Netherlands may have recorded the first known cases of animal-to-human transmission of coronavirus at a mink farm, the World Health Organization (WHO) has said.
The WHO said it was reviewing the cases of two Dutch mink-farm workers who appear to have contracted Covid-19 from the animals.
On Monday, Dutch Agriculture Minister Carola Schouten announced the second suspected infection of an employee at a mink farm.
“These would be the first known cases of animal-to-human transmission," a WHO spokesperson told AFP news agency on Tuesday.
“But we are still collecting and reviewing more data to understand if animals and pets can spread the disease.”
The first cases of the coronavirus were linked to a market where wild animals were sold in the Chinese city of Wuhan. Exactly where the virus came from remains a mystery, but most disease experts agree the virus was transmitted to humans by an animal, possibly a bat.
Until the suspected mink-farm transmission in the Netherlands, there have been no instances of animals infecting humans with Covid-19 since the disease emerged.
However, the WHO said evidence suggests “other animal species are also susceptible to the virus and can be infected, including cats, ferrets”.
Read more: Can my dog or cat catch coronavirus?
Samira Hussain
New York business correspondent
Image source, ReutersThe New York Stock Exchange (NYSE) is set to reopen its trading floor on Tuesday
Before the coronavirus, I was a regular on the floor of the New York Stock Exchange.
It may be one of the great symbols of US capitalism, but it's also just a workplace for hundreds of traders, market makers and various bystanders - such as journalists!
And, like so many offices and shop floors, it's not somewhere that you would ever associate with social distancing, keeping two metres apart and wearing masks.
Quite the reverse - face-to-face stock trading is sometimes close to a contact sport, as is reporting from the floor.
So the NYSE has to take its "reopening" very slowly. It will be a relief for some traders to be back to work, but it's not going to look like the trading floor we're all used to seeing for quite some time.
Image source, Getty ImagesThe biggest football game of the German season takes place tonight as Borussia Dortmund host rivals Bayern Munich in the game known as Der Klassiker.
The match - which would usually be played in front of about 80,000 fans - will instead be behind closed doors at Dortmund's Signal Iduna Park.
Dortmund are only four points behind Bayern, who have won seven consecutive Bundesliga titles, so this match could have a huge impact in the title race.
Among the star players who will be on show are Robert Lewandowski, Erling Braut Haaland and England's Jadon Sancho.
The game kicks off at 17:30 BST (16:30 GMT) with live text commentary on the BBC Sport website.