The Conservative leader spent three days in intensive care after contracting the virus, and has been off work since March 27, but was released from hospital last Sunday after a week-long stay.
Britain's official death toll from the virus now stands at 16,060 after 596 more deaths were reported Sunday, and the country has been under lockdown since March 23, with the government extending it until at least the end of the month.
Education minister Gavin Williamson said on Sunday that "I can't give you a date" as to when schools would reopen.
Recent figures suggest the outbreak in Britain was "starting to plateau", said Jenny Harries, Deputy Chief Medical Officer for England, but warned it was "not fair to say we are past the peak".
Senior minister Michael Gove earlier sought to defend Johnson after the prime minister was accused of being "missing in action" in the early stages of the outbreak.
Johnson "is absolutely on top of things" and issuing instructions, Gove told Sky News. "The prime minister is recovering well, he is in cheerful spirits."
His comments came after a Sunday Times newspaper report said Johnson had missed five of the government's emergency response meetings in January and February.
"None of us expect the impossible, but there are serious questions about why the prime minister skipped Cobra meetings," the opposition Labour Party's shadow health minister Jonathan Ashworth told Sky News.
"It suggests early on he was missing in action."
>> 'Grave concerns' about Covid-19 immunity passports
Gove claimed there were inaccuracies in the Sunday Times report, which was based largely on unnamed civil service sources, and that the government would issue a rebuttal.
"The idea that the prime minister 'skipped' meetings, I think, is grotesque, there are meetings across government, some chaired by the health secretary, some chaired by other ministers," he said.
"The prime minister took all the major decisions. Nobody can say that the prime minister wasn't throwing heart and soul into the virus."
Williamson also defended his boss, saying he "has absolutely been leading our effort" to fight the virus.
The government is also under pressure over shortages of personal protective equipment (PPE) for frontline health workers, with warnings that gowns could run out within days.
Chaand Nagpaul, chair of the council of the British Medical Association (BMA), told Sky that 50 percent of doctors are saying they feel they don't have adequate protection.
"The government hasn't been as agile as it should have been," he added.
"This is extremely emotionally taxing and it's showing its toll on the healthcare workforce."
Gove said PPE was the government's "first priority" and suggested that 25 million gowns would be arriving from China "in due course".
"Gowns are the area at the moment where there is the greatest need," he said.
Downing Street announced on Sunday that Paul Deighton, the former London Olympics chief, has been appointed to lead the effort to domestically produce PPE.
But it later emerged that a large shipment of PPE from Turkey had been delayed, with Williamson saying "we hope to see it come in the country tomorrow".
On the lockdown, Gove said: "We shouldn't be thinking of lifting these restrictions now.
"One of the things that is deeply worrying and concerning is still the high level of deaths," he said.
"We're not absolutely certain that we are yet on a downward trajectory (of infections) and we want to be heading towards that downward trajectory to be confident about all the steps we might want to take."