.jpg )
The PM is being kept at St Thomas' Hospital in London "for close monitoring", Downing Street said.
Mr Johnson's condition is "stable" and he remains in "good spirits", his spokesman added on Tuesday evening.
Downing Street also confirmed that the planned review into whether the UK's coronavirus restrictions could be eased would not go ahead this Monday.
Foreign Secretary Dominic Raab, who is deputising for the PM, has said he was "confident" the PM would recover from this illness, describing him as a "fighter".
Speaking at Tuesday's Downing Street coronavirus briefing, he said Mr Johnson was receiving standard oxygen treatment and was breathing without any assistance, such as mechanical ventilation or non-invasive respiratory support.
It is understood there will not be a further update on Mr Johnson's condition until later on Wednesday.
Meanwhile, the first patients have been admitted to the NHS Nightingale Hospital in east London - a temporary facility set up at the ExCel conference centre.
The admissions come two weeks after the hospital with a planned capacity of 4,000 was formally announced - although an NHS spokesperson stressed limits had not been reached at other sites in London.
The prime minister was originally admitted to St Thomas' on Sunday, on the advice of his doctor, after continuing to display symptoms of cough and high temperature 10 days after testing positive for the virus.
Mr Raab said the prime minister was being monitored closely in critical care, as was usual clinical practice.
Describing Mr Johnson as not only a boss but "also a friend", Mr Raab said: "All of our thoughts and prayers are with the prime minister at this time, with Carrie, and with his whole family.
"And I'm confident he'll pull through, because if there's one thing I know about this prime minister, he's a fighter. And he'll be back at the helm, leading us through this crisis in short order."
Buckingham Palace said the Queen had sent a message to Mr Johnson's family and his pregnant fiancee, Carrie Symonds, saying she was thinking of them, and wished the PM a full and speedy recovery.
Prince William also tweeted a personal message of sympathy to the PM's family, signing it off with his initial "W", while his father, the Prince of Wales, sent a message from himself and the Duchess of Cornwall wishing Mr Johnson a "speedy recovery", Clarence House said.
At the briefing, Mr Raab was also asked about whether his role deputising for Mr Johnson gave him full prime ministerial responsibility.
The foreign secretary said he was standing in for the prime minister "whenever necessary" - including leading the daily meetings of the coronavirus "war cabinet".
He said decisions would be made by "collective cabinet responsibility - so that is the same as before".
"But we've got very clear directions, very clear instructions from the prime minister, and 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," Mr Raab added.
A ban on public gatherings of more than two people and the closure of shops selling non-essential goods were among the series of restrictions announced by Mr Johnson on 23 March to tackle the spread of coronavirus. He had said a relaxation of the rules would be considered in three weeks, which would be 13 April.
But Mr Raab said: "The critical thing is to take evidence-based decisions and so we've said that we will take any review once we've got the evidence that the measures are working.
"And having the kind of impact taking us past the peak which means that they can be responsibly done. We're not at that stage yet."
Downing Street later confirmed that the review would not go ahead on the scheduled date and would instead take place after the three-week mark.
It came as the number of coronavirus hospital deaths in the UK rose to 6,159 on Tuesday - a record increase of 786 in a day, the Department of Health and Social Care said, compared with 439 on Monday.
However, the government's chief scientific adviser told the Downing Street briefing the number of coronavirus cases in the UK "could be moving in the right direction".
Sir Patrick Vallance said it was "possible that we're beginning to see... the curve flattening".
As of 09:00 BST on Tuesday, 213,181 people have been tested, of which 55,242 tested positive, the Department of Health and Social Care said.
Overall, 266,694 tests have been concluded, with 14,006 tests carried out on Monday.