Boris Johnson has denied saying he would rather see "bodies pile high in their thousands" than have another COVID lockdown.
The prime minister rebuffed newspaper allegations that he had made the comments in October, just prior to England's second national lockdown.
The Daily Mail on Monday reported that Mr Johnson exclaimed after a Number 10 meeting at the time: "No more ****ing lockdowns - let the bodies pile high in their thousands!"
But, asked if he had ever made those remarks during a visit to Wrexham at Monday lunchtime, the prime minister said: "No.
"The important thing I think people want us to get on and do as a government is to make sure that the lockdowns work and they have.
"I really pay tribute to the people of this country, this whole country of ours, that have really pulled together and - working with the vaccination programme - we've got the disease under control."
His version of events was backed up by Michael Gove, who serves in Mr Johnson's Cabinet as minister for the Cabinet Office.
Mr Gove told Parliament, in a debate about the ministerial code: "The idea that he would say any such thing I find incredible. I was in that room. I never heard language of that kind."
A report in the Spectator magazine, however, suggested Mr Johnson made the remark in his study just after he agreed to the second lockdown.
During his trip to Wrexham, Mr Johnson warned the public needed to be "realistic" as "there will probably be another wave" of COVID infections.
But he said the UK's "massive" vaccine programme - which has now seen more than 33.6 million people receive a COVID jab - had "built up what I think are some pretty robust fortifications against the next wave".
"We'll have to see how strong they really are in due course," he added.
"But in the meantime, everybody should come forward and get your get your vaccine when you're asked."
The Daily Mail reported Mr Johnson's alleged comments were made at the end of October as the UK was hit by a second wave of coronavirus infections.
According to the newspaper, the prime minister was given a warning by Mr Gove that - without new restrictions - soldiers would be needed to guard hospitals overrun with COVID patients.
Mr Johnson agreed to fresh measures but also vented his frustration at having to implement tough measures again, said the Daily Mail's account.
On 31 October last year, the prime minister announced a month-long lockdown in England throughout November.
After a brief reopening, England went back into a national lockdown again - the third - in January, as ministers highlighted the impact of the Kent variant of the virus.
The allegation about Mr Johnson's comments in October comes amid a bitter feud between Downing Street and the prime minister's former chief adviser, Dominic Cummings.
Last week, Number 10 "sources" were quoted in newspapers as blaming Mr Cummings for recent leaks about the prime minister's private conversations.
But Mr Cummings hit back and denied "false accusations".
Asked about the reports of Mr Johnson's alleged comments in October, defence secretary Ben Wallace told Sky News earlier on Monday: "We're getting into the sort of comedy chapter now of these gossip stories - unnamed sources by unnamed advisers talking about unnamed events.
"None of this is serious."
Mr Wallace said Mr Johnson and his cabinet ministers had been "utterly focused" on their response to the COVID crisis.
"All the 'who said, what said, what said', I'll leave that to the Oscar gossip columns that are now being rolled out today after last night, I'll leave that to the Hello magazines of the world," he added.
During the debate on the ministerial code Mr Gove's opposite number, Labour's Rachel Reeves, told the Commons, while asking a series of questions: "As for leaks, we are seeing the pipes burst with a suite of allegations...
"This is a prime minister who would rather that the bodies pile high than act on scientific advice. Mr Speaker, they are not bodies. They are people. They are loved ones, and they are deeply missed...
"Will the minister apologise for the stomach churning comments that have come out today and urgently announce a public enquiry into the government's handling of the pandemic? Because this is all about conduct, character and decency. And frankly, our country deserves better than this one."
Mr Gove said later that, in the meeting in which the comments were said to have been made, Mr Johnson ordered the second national lockdown, and went on to order a third.