Another Conservative MP has called for Boris Johnson to resign as the turmoil at 10 Downing Street continues, reports BBC.
Former minister Nick Gibb is the latest Tory to submit a letter of no confidence in the row over events held at No 10 during lockdown.
He said his constituents were furious that No 10 had been "flagrantly disregarding" the Covid rules they set.
But Culture Secretary Nadine Dorries insisted the "vast majority" of Conservative MPs supported Mr Johnson.
Meanwhile, the Daily Mirror reports a photograph of Mr Johnson holding a beer at a birthday gathering has been handed to police investigating Covid breaches.
The paper said the picture was one of 300 submitted to the Metropolitan Police investigation into 12 alleged gatherings and was thought to have been taken by the PM's official photographer, who is funded by the taxpayer.
It said it showed the prime minister holding a can of beer at an event in No 10's Cabinet Room in June 2020, alongside Chancellor Rishi Sunak, who was holding a soft drink.
At the time, gatherings of more than two people inside were banned by law.
It comes at the end of a difficult week for the PM, which has seen five No 10 aides resign and the publication of the initial findings of the Sue Gray report into events at Downing Street while Covid restrictions were in place.
Writing in the Daily Telegraph, Mr Gibb, who has served under three prime ministers and who lost his position as schools minister in Boris Johnson's reshuffle last September, said his constituents were "furious about the double standards" and that "to restore trust, we need to change the prime minister".
He said Covid restrictions imposed by Mr Johnson were "flagrantly disregarded" in Downing Street, and the PM was inaccurate when, in December, he told the House of Commons there was no party.
"Some argue that eating a few canapes with a glass of prosecco is hardly a reason to resign. But telling the truth matters, and nowhere more so than in the House of Commons where, like a court of law, truth must be told regardless of the personal consequences," he wrote.
Mr Gibb said fellow backbench Tory Aaron Bell had "struck a chord" when he criticised Mr Johnson over lockdown parties earlier this week.
Mr Bell had asked the prime minister if he took him for a fool for following the rules himself - including not hugging his family at his grandmother's funeral, or going for a cup of tea after the service.
On Friday, Mr Bell said the "breach of trust" over the rule breaking and how it had been handled made the PM's position untenable, as he confirmed he had also submitted a letter of no confidence to Sir Graham Brady - the chair of the 1922 Committee of backbench MPs.
At least 54 MPs need to write to Sir Graham to trigger a vote on the PM's leadership of the party.
Other Conservative MPs are expected to consider whether to put in their letters over the weekend.
Mr Johnson has written to all Tory MPs to say he is committed to improving the way 10 Downing Street works.
Ms Dorries told the BBC most MPs were "right behind the prime minister because he has delivered... and will continue to do so" and said Mr Johnson had been "very positive" when she communicated with him within the past 24 hours.
She said a huge amount of change was now under way within No 10, but she was "cautious" of asking him to change too much, because of achievements such as having the biggest majority since Margaret Thatcher.
Ms Dorries said those speaking out against Mr Johnson were "the same names" that "keep cropping up" and "no prime minister would please any of those".
She said there were "a few voices being amplified" by the media, describing the comments made by Mr Gibb and Mr Bell as "disappointing".
Speaking on Newsnight, Conservative MP Andrew Bridgen suggested it was now the job of the cabinet to "show leadership" and "confront" the issue of the prime minister's leadership.
But his fellow Tory MP Richard Bacon suggested it was not for politicians to change governments - that was for the electorate to take care of.
And Liam Fox, former trade secretary, said there was a danger the party was becoming distracted from big issues such as inflation, the energy crisis and the situation in Ukraine.
He told BBC Radio 4's Today programme: "There will need to be closure on this issue, in the Conservative Party and in the country, and I think when there's more to say, we should say it, and there are questions that will need to be answered."
Some of Mr Johnson's supporters, including one former cabinet minister, have criticised the Chancellor Rishi Sunak, who this week distanced himself from the prime minister's controversial comments about Sir Keir Starmer, for being disloyal at a difficult time.
No 10 policy chief Munira Mirza quit on Thursday, describing Mr Johnson's comments on Sir Keir as "scurrilous".
The prime minister falsely claimed the Labour leader had failed to prosecute paedophile Jimmy Savile during his time as director of public prosecutions.
Mr Sunak said he "wouldn't have said it", while on Friday Health Secretary Sajid Javid said Sir Keir "did a good job and should be respected for it".
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