Boris Johnson suggested that “bodies could pile high” during a heated discussion about lockdown in Downing Street in the autumn, sources familiar with the talks have told the BBC.
On Monday, the Daily Mail reported that Mr Johnson had said “let the bodies pile high in their thousands” rather than order a third lockdown.
The PM denied making the remarks, adding that lockdowns had worked.
Labour leader Sir Keir Starmer said he was “astonished” by the reports.
He added that: “Everybody would be deeply concerned, not least all those families who have lost someone in the pandemic.”
The comments are said to have been made at the end of October when England went into its second lockdown following a sharp rise in coronavirus cases.
BBC political editor Laura Kuenssberg says, at the time, the prime minister was reported to have had big concerns about the implications of another lockdown on the economy and non-Covid related health issues.
“This does take us back to that moment and back to the very serious claims made by some people who were involved in the decision making – including some ministers – that the hesitancy around the second lockdown did cost lives,” she said.
The story was labelled “not true” by Defence Secretary Ben Wallace and when asked about the comments earlier on Monday, Mr Johnson denied having made them.
He added that the public wanted the government “to make sure that the lockdowns work, and they have,” he said.
The PM’s spokesman also said the reported comments were false adding: “This is untrue and the PM has denied it… I’m not aware of anyone else making that statement.”
This comes amid a bitter row between Downing Street and the prime minister’s former senior adviser Dominic Cummings.
Last week Mr Cummings published a blog in which he denied leaking information about the second lockdown in England to the press and said he had been cleared by the top civil servant Simon Case.
Mr Cummings also alleged Mr Johnson considered blocking an inquiry into the leak in case it involved a friend of his fiancee Carrie Symonds.
Mr Case is giving evidence at an MPs’ committee and has said the inquiry is ongoing, however he added that “given the time that has now passed, I think it’s probable the team will not successfully identify the source or sources”.
A Cabinet Office source told the BBC that no-one had yet been exonerated in the investigation.