Video report by ITV News Political Editor Robert Peston
Prime Minister Boris Johnson will be spending another night at St Thomas' Hospital where he is being treated for coronavirus.
"The Prime Minister’s condition is stable and he remains in intensive care for close monitoring. He is in good spirits,” a Number 10 spokesman confirmed.
US President Donald Trump has described Mr Johnson's admittance to critical care as "shocking".
Mr Trump said: "Intensive care is a big deal with regard to what we're talking about. That's a very big deal. A very scary deal."
The US President's comments come as the NHS Nightingale hospital confirmed the first patients have been admitted to the hospital in London which was created to boost capacity during the coronavirus outbreak.
Earlier Foreign Secretary Dominic Raab said Mr Johnson is a "fighter" who will be back from intensive care to lead the country's battle against coronavirus in "short order".
Mr Raab, taking the lead at the government's daily Covid-19 press conference, said he is "confident" his boss will be back soon.
"If there's one thing I know about this prime minister, he's a fighter and he'll be back at the healm leading us through this crisis in short order."
He said all ministers wish Mr Johnson a speedy recovery in hospital, saying: "He's not just our boss, he's also a colleague and he's also our friend".
'Boris Johnson will feel as if he’s letting the country down': George Osborne discusses the prime minister and coronavirus
Meanwhile the first secretary of state, who is standing in for the prime minister while he battles coronavirus in hospital, said he has "total confidence" in the arrangements that allow him to "deputise" for Mr Johnson.
Mr Raab said that the Cabinet has "very clear instructions" from the prime minister while he battles the virus.
"We're focused with total unity and total resolve on implementing them so that when he's back, I hope in very short order, we will have made the progress that he would expect and that the country would expect."
"This team will not blink and will not flinch at the task in hand at this crucial moment", Mr Raab added.
He had been moved to intensive care after his consistent coronavirus symptoms worsened while having tests in hospital.
Mr Raab said the prime minister is "receiving the very best care" while in hospital and has "not required any mechanical ventilation or non-invasive respiratory support".
The latest Department of Health (DoH) figures cover cases up to 5pm on Monday and mark an increase of 786 from 5,373 the day before.
In addition, the DoH said that, as of 9am on Tuesday, 213,181 people have been tested, of which 55,242 tested positive.
Overall, 266,694 tests have been concluded, with 14,006 tests carried out on Monday.
At the press conference positive signs in the battle against coronavirus were pointed to, but with caution.
The Government's chief scientific officer Sir Patrick Vallance said the number of new cases "could be moving in the right direction" but it would not be clear "for a week or so".
He said evidence shows the UK is "beginning to see the beginning of change in terms of the curve flattening a little bit".
He went on: "There hasn't been the accelerated take-off and again it's possible that we're beginning to see the start of a change where we might see numbers flattening off.
"It does begin to suggest that things might be moving in the right direction in terms of numbers and it's important that we carry on with the measures that we have got in place in order to make sure that this does go in the right direction."
What happens in an intensive care unit? Watch below
Former prime minister David Cameron sent his best wishes to Mr Johnson, saying he is "hoping and praying" for a full recovery so the PM can "get in charge again".
He told ITV News Mr Johnson is a "very tough, very resilient, very fit person," adding, "I'm sure he'll get through this".
It was earlier revealed that if Mr Raab too is debilitated by the virus, Chancellor Rishi Sunak will step in.
The Prime Minister’s official spokesman said there was an "established order of precedence" which would dictate which ministers would follow if Mr Raab was also incapacitated.
As First Secretary of State - effectively deputy prime minister - as well as being Foreign Secretary, Mr Raab was top of the list to deputise for Mr Johnson after he was hospitalised.
The spokesman said after that, Mr Sunak was the next in line.