Boris Johnson on Monday appeared to claim he forced out Matt Hancock, despite his press team briefing that the former health secretary quit of his own accord.
Downing Street told reporters Mr Hancock had not been pressured to go after he resigned following revelations that he was having an affair with an aide.
But with broadcasters questioning ministers about why the Prime Minister had not acted over the scandal, Mr Johnson suggested in an interview that he had intervened.
He said: "I read the story on Friday and we’ve got a new Health Secretary in post on Saturday, and I think that’s about the right pace to proceed in a pandemic."
The comment triggered accusations that he was rewriting history, given that he had initially stood by Mr Hancock when the news broke.
Tory MPs feared a public backlash over Mr Hancock urging people to abide by Covid rules while breaching social distancing rules himself. But friends of the former health secretary are urging him to plot his route back to the Cabinet, suggesting that he champions policy causes from the backbenches to rebuild his reputation.
Mr Johnson’s comments added to the confusion over Mr Hancock’s departure and the degree to which it was his own decision rather than being urged by Number 10.
Overnight on Thursday, The Sun revealed that Mr Hancock had been having an affair with Gina Coladangelo, publishing a photograph showing them kissing.
On Friday, Downing Street initially briefed journalists that Mr Johnson had accepted an apology from Mr Hancock for breaching social distancing and considered the matter closed. Then, late on Saturday, Mr Hancock resigned. Mr Johnson said in his letter of response that he was "sorry" to see his health secretary leaving.
On Sunday, Downing Street figures argued that Mr Johnson had not put pressure on Mr Hancock to resign, but the Prime Minister suggested otherwise on Monday.
But on Monday afternoon, Mr Johnson’s official spokesman appeared to be walking back his comments with a clarification during a press briefing. The spokesman denied the Prime Minister had a role in Mr Hancock’s departure, adding that he "felt it was the right decision" to accept the resignation.
Angela Rayner, the Labour deputy leader, said: "Boris Johnson is trying to rewrite history because he didn’t have the guts to sack Matt Hancock. A fish rots from the head down and, by failing to sack the former health secretary, Johnson proved he doesn’t have the leadership qualities or judgment required to be Prime Minister."
Separately, Dominic Cummings threatened to release evidence showing that ministers have used personal accounts to conduct government business during the pandemic. The former Number 10 aide challenged Downing Street after it denied Mr Hancock had routinely used a personal email address to conduct official business since March last year.
Mr Cummings described the denial as "nonsense", adding that he had screenshots proving that both Mr Hancock and Mr Johnson had used the messaging service WhatsApp to discuss "procurement issues" with a "Tory donor network".
On Monday night, allies of Mr Hancock urged him to plot a path back to the Cabinet by showing "deep commitment" to a cause linked to his former brief.
One Tory MP who backed him for party leader in 2019 said: "He should take something from the health portfolio and make it his own, like mental health or social care. Like Iain Duncan Smith, who went off to the housing estates of Glasgow and discovered poverty [after leaving the front bench], he can go off around the country, interview people, make a Portillo-ite film."
The MP predicted that, by following this strategy, Mr Hancock could orchestrate an "impressive rehabilitation".
Another supporter suggested it would make sense for him to focus on global health security, capitalising on the knowledge he had developed during the pandemic. The source added: "He’s got a huge range of interests and he’s always been someone who can make a positive contribution to public debate."
However, it is understood that for now Mr Hancock intends to return to his constituency and focus on his work as an MP.