The foreign secretary says he is “confident” the prime minister will “pull through” after he was put into intensive care on Monday.
Dominic Raab, who is now formally deputising for Boris Johnson, was speaking at the daily Downing Street coronavirus briefing on Tuesday.
He reiterated that the prime minister “remains in good spirits” and was breathing without assistance, although he has received oxygen support.
The foreign secretary spoke of Mr Johnson as a “friend” as he noted the “groundswell of support” that had been offered to the prime minister since Monday night.
He added: “As will be the case for many people up and down the country who know someone at work who has fallen ill with coronavirus, it is a shock to all of us.
“He is not just the prime minister. For all of us in cabinet, he is not just our boss.
“He is also a colleague and he is also our friend. So all our thoughts and prayers are with the prime minister at this time, with Carrie [Symonds] and his whole family.
“And I’m confident he will pull through because if there is one thing that I know about this prime minister [it] is he is a fighter and he will be back leading us through this crisis in short order.”
Mr Raab said he and fellow cabinet ministers “will not blink or flinch” in the battle against COVID-19, despite Mr Johnson’s absence.
The foreign secretary said cabinet ministers had “very clear directions, very clear instructions” from the prime minister.
“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,” he added.
Mr Raab dodged questions about whether he had full decision-making authority while Mr Johnson is indisposed.
He instead stressed there are “collective cabinet responsibilities” for decision-making.
Appearing alongside Mr Raab at the news conference, Sir Patrick Vallance – the government’s chief scientific adviser – said the UK “might be moving in the right direction” in terms of the number of new coronavirus cases.
“It’s possible that we’re beginning to see the beginning of change in terms of the curve flattening a little bit,” he said.
“We won’t know that for sure for a week or so.
“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.”
But Mr Raab said the government would not yet be reviewing the lockdown measures in the UK – aimed at slowing the spread of coronavirus – as he urged Britons to stay at home over the Easter weekend.
“The worst thing now would be to take our foot off the pedal, to ease up on that and risk losing the gains that have been made,” he said.
England’s chief medical officer, Professor Chris Whitty, admitted there was “a lot to learn” from the coronavirus response in Germany, where the rate of growth in the number of COVID-19 deaths appears to be much slower.
“We all know that Germany got ahead in terms of its ability to do testing for the virus and there’s a lot to learn from that and we’ve been trying to learn the lessons from that,” he said.
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Germany is estimated to be conducting more than 50,000 coronavirus tests a day. On Monday, 14,006 coronavirus tests were carried out in the UK.
Mr Raab said the government’s target of reaching 100,000 tests per day by the end of this month “still stands”.
The UK appears to be following a similar death rate trajectory to Italy, but Sir Patrick said this does not mean the two countries will end up with the same end result.
“We are probably three or four weeks behind Italy in terms of the outbreak,” he said. “It doesn’t mean we end up with the same numbers.”
Mr Johnson was initially admitted to hospital on Sunday night but his condition worsened on Monday afternoon – more than a week after he tested positive for coronavirus.
The prime minister’s official spokesman revealed earlier on Tuesday that Mr Johnson was “stable” overnight, had not required a ventilator and had not been diagnosed with pneumonia.
The Queen has sent a message to Mr Johnson’s family and the prime minister’s pregnant fiancee Ms Symonds, saying they were in her thoughts and that she wished Mr Johnson a full and speedy recovery.
Mr Raab chaired the daily morning meeting of the government’s coronavirus “war cabinet” for the second day in a row earlier on Tuesday.