The Cabinet Office minister said on Monday that he “never heard language of that kind” in the meeting where Mr Johnson ordered the second shutdown in England.
Mr Johnson was accused of having made the remarks after agreeing to a second lockdown, suggesting he was prepared to face a mounting death toll rather than order a third set of tough restrictions.
“The idea that he would say any such thing I find incredible,” Mr Gove told the Commons.
He added that “I was in that room, I never heard language of that kind”, in a defence stopping short of a full denial that the comments had been made.
However, an ITV report suggested Mr Johnson made the remark in his study just after he agreed to the second lockdown.
Labour’s shadow chancellor of the Duchy of Lancaster Rachel Reeves said: “The Prime Minister is now corrupting the standards of public life expected in high office.”
The Daily Mail first carried the claim that, following a decision on the second lockdown, the Prime Minister said he would rather see “bodies pile high in their thousands” than order a third one.
The paper did not name the source for the allegation, which was later also reported by the BBC citing “sources familiar with the talks”, but ministers hit out at “gossip” spread by “unnamed advisers”.
Asked if he made the comments, Mr Johnson told reporters in Wrexham: “No, but I think the important thing I think people want us to get on and do as a Government is to make sure that the lockdowns work.
“They have, and I really pay tribute to the people of this country, this whole country of ours, really pulled together and, working with the vaccination programme, we have got the disease under control.”
He insisted the “stuff that people are talking about” in Westminster were not issues being raised on the doorstep ahead of the May 6 elections.
The decision on the second lockdown last autumn was leaked and is the subject of an inquiry to find the so-called “chatty rat” who tipped off the press.
Appearing before MPs, the UK’s most senior civil servant declined to say whether Mr Johnson’s former adviser Dominic Cummings had been cleared over that leak, as the former aide has claimed.
Cabinet Secretary Simon Case told the Public Administration and Constitutional Affairs Committee (PACAC) that it is “probable” that the culprit will never be identified.
But he said the Prime Minister did not try to block the investigation, after his former Vote Leave ally alleged he had considered the move.
Mr Cummings accused Mr Johnson of seeking to block the investigation after learning that a close friend of his fiancee Carrie Symonds had been implicated, a claim the Prime Minister denied.
In an incendiary blog post, Mr Cummings went on to say that Mr Case had told Mr Johnson that neither he nor the then No 10 director of communications, Lee Cain, was the culprit.
The Cabinet Secretary declined to comment on the suggestion, telling the MPs: “I am not trying to frustrate, but this is drawing me into details of an ongoing investigation which – for reasons I have set out – I can’t go into in this setting.”
Asked by chair William Wragg if an outcome had been “actually desired”, Mr Case said that “from the outset” the Prime Minister and others were “determined” to find the culprit.
Pressed if he knew of an investigation being stopped because the outcome would be embarrassing, Mr Case said: “No, in relation to this particular leak and others, the Prime Minister has always been clear, very determined to see these inquiries complete.”
Mr Cummings released his onslaught after he was accused by No 10 of a series of damaging leaks, including text message exchanges between Mr Johnson and the entrepreneur Sir James Dyson.
Ministers are now concerned at what he may say when he gives evidence to MPs investigating the Government’s response to the pandemic next month.
Mr Cummings is widely known to have been critical of Mr Johnson’s delay in launching a second lockdown in England when cases began rising last autumn, and there is speculation he will seek to blame him for the high death toll.
In a sign the allegations of sleaze and cronyism levelled at the Government may be having an impact, an Ipsos Mori poll for the Evening Standard showed that Conservative support had fallen by five points since last month.
The poll put the Tories on 40%, Labour on 37%, down one point, the Liberal Democrats up two points on 8% and the Greens unchanged on 5%.
The polling was carried out from April 16-22, before the latest row between No 10 and Mr Cummings.
Labour leader Sir Keir Starmer said it was time for “a full and transparent investigation into everything that’s going on” in No 10.
Speaking on a visit to the West Midlands, he said: “Day after day there are new allegations of sleaze, of favours, of privileged access.”