Home Secretary Priti Patel has told Conservative MPs pushing for Boris Johnson to resign to "forget it".
Patel said writing letters of no-confidence in the Prime Minister was a "sideshow" and the party should be focused on "real challenges that we have to find solutions to".
Speaking to the Daily Mail, she said: "This isn't about a parade (of leadership candidates) or a contest of letters. We need to concentrate on doing our jobs.
"Look at what is going on in the world right now, look at the challenges that we face domestically. We can't ignore those.
"Our job is to deliver on the people's priorities. They won't thank the Conservative Party for talking about itself at a time when people have anxieties, concerns, apprehensions."
Patel also said she thought leadership rows should not overshadow the Platinum Jubilee celebrations.
Earlier, Boris Johnson claimed quitting as Prime Minister over the "miserable" partygate scandal would be irresponsible and denied suggestions he is a "habitual liar".
He cited "huge pressures" on the economy, the war in Ukraine and his "massive agenda which I was elected to deliver" as his reasons for remaining in his post and not seeking to "abandon" ship.
But Johnson is under increasing pressure from Tory MPs to consider his position in the wake of Sue Gray's report on lockdown parties in Downing Street.
Simon Fell, elected Conservative MP for Barrow and Furness in 2019, was the latest to be reported to have raised concerns and criticised the "corrosive culture and a failure of leadership" that allowed the incidents to happen.
Johnson's own ethics adviser also criticised his handling of partygate, with Lord Geidt suggesting Johnson's fixed penalty notice (FPN) may have breached the ministerial code.
Lord Geidt, the independent adviser on the ministerial code, said a "legitimate question" had arisen as to whether the FPN, issued for a June 2020 birthday party thrown in Johnson's honour in the Cabinet Room, might have constituted a breach of the "overarching duty within the ministerial code of complying with the law".
Deputy Prime Minister Dominic Raab led the counter-attack on Wednesday by insisting questions around whether Johnson broke the rules for ministers "have been answered", as he backed the PM's assertion that he did not intend to breach Covid laws.
The Justice Secretary said he does not believe the Prime Minister will face a confidence vote next week, as the prospect of a leadership challenge loomed.
Johnson, in an interview with Mumsnet released on Wednesday, was initially told he was considered to be a "habitual liar".
The Prime Minister replied: "First of all, I don't agree with the conclusion with the question asked or the premise of the question."
Told a teacher would have lost their job if they had broken the law and asked why the same did not apply to him, Johnson replied: "If people look at the event in question it felt to me like a work event, I was there for a very short period of time in the Cabinet Office at my desk and, you know, I was very, very surprised and taken aback to get an FPN but of course I paid it.
"I think that on why am I still here, I'm still here because we've got huge pressures economically, we've got to get on, you know, we've got the biggest war in Europe for 80 years, and we've got a massive agenda to deliver which I was elected to deliver.
"I've thought about all these questions a lot, as you can imagine, and I just cannot see how actually it'd be responsible right now - given everything that is going on simply to abandon... the project which I embarked on..."
Sir Geoffrey Clifton-Brown, treasurer of the backbench 1922 Committee, said Conservative MPs need to consider which "crimes" Johnson has "actually committed" before launching a leadership coup.
So far, more than 25 MPs have publicly called on the Prime Minister to stand down - although not all of them have said whether they have written to Sir Graham.
Culture Secretary Nadine Dorries told BBC Radio 4's World at One programme that efforts to topple the Prime Minister are being co-ordinated by "one or two individuals" for reasons of "personal ambition".
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