The prime minister is breathing without a ventilator and has not been diagnosed with pneumonia, Downing Street has said.
His spokesman said Boris Johnson was stable overnight and remains in good spirits.
The PM’s spokesman said Mr Johnson had been receiving standard oxygen treatment but had not required any other help with his breathing.
Meanwhile, the Queen has sent a message to Mr Johnson’s family and his pregnant partner Carrie Symonds, saying they were in her thoughts and that she wished the PM a full and speedy recovery.
And in a message posted on the Kensington Palace Twitter account, Prince William said: Our thoughts are with the prime minister and his family, who like so many in the UK and around the world are affected by coronavirus. We wish him a speedy recovery at this difficult time.
It comes as it was confirmed that another 758 patients have died in England after contracting the coronavirus – bringing the total to 5,655.
Mr Johnson was initially admitted to St Thomas’ Hospital in London on Sunday evening, but his health deteriorated during the course of Monday.
The precautionary decision to move him to intensive care was taken on the advice of his medical team at around 7pm, with Downing Street revealing the news in a statement an hour later.
It is understood Mr Johnson remained conscious at the time of the announcement and was moved to intensive care as a precaution should he require ventilation to aid his recovery.
Cabinet Office minister Michael Gove told LBC earlier that the PM has not been on a ventilator but has received oxygen support.
Mr Johnson’s spokesman rejected claims that Number 10 had tried to hide the seriousness of his condition.
We have been fully frank with you throughout, he told reporters during the government’s daily media briefing.
We have issued you with regular updates on the prime minister’s health.
His condition worsened yesterday afternoon. A decision was taken that he needed to be moved to an intensive care unit at around 7pm.
We informed you all as soon as was practically possible. We have a commitment to be as transparent as we can be throughout this process.
Downing Street confirmed that weekly calls between Number 10 and the Queen will not take place during Mr Johnson’s hospital stay.
Foreign Secretary Dominic Raab, who is deputising for the PM, will not be asked to step-in to brief the monarch on behalf of Mr Johnson.
Buckingham Palace and Her Majesty the Queen have been kept regularly informed about the prime minister’s condition and that will continue, Mr Johnson’s spokesman said.
The cabinet secretary and the prime minister’s principal private secretary will continue their contacts with the Royal Household on the prime minister’s behalf.
Asked if Mr Raab would field any phone calls with the Queen, the spokesman responded: No, it has been agreed with the Royal Household that weekly audiences will not go ahead.
(c) Sky News 2020: Coronavirus: Boris Johnson breathing without a ventilator in intensive care, Number 10 says