The Prime Minister apologized for handling the 2020 Downing Street garden event and said he understood the public's "rage" about it.
Cabinet officials, including Deputy Prime Minister Dominic Raab, came to Johnson's defense.
However, Scottish Conservative leader Douglas Ross and prominent backbenchers William Wragg and Caroline Nokes have urged him to go.
Ross, both a Member of Parliament and a Member of the Scottish Parliament, said he had a "difficult conversation" with Johnson following the Prime Minister's apologies to MPs earlier on Wednesday.
He stated that he would write to the 1922 Committee, which arranges Tory leadership races, to express his dissatisfaction with the Prime Minister.
"He is the prime minister, it is his government that put these rules in place, and he has to be held to account for his actions," he stated.
A leadership challenge will be triggered if 54 Conservative backbenchers write to the 1922 committee.
Ministers have encouraged MPs to hold off on voting until an investigation into potential COVID rule violations at Downing Street parties by senior civil servant Sue Gray is released.
However, another Conservative backbencher, William Wragg, who chairs a powerful select committee, declared the prime minister's situation "untenable."
"I don't think it should be left to the findings of a civil servant to determine the future of the prime minister and indeed who governs this country," he told BBC Radio 4's PM program.
And Conservative colleague Caroline Nokes, who leads another Commons committee, said the prime minister should step down immediately because he was "damaging the entire Conservative brand."
Previously critical of Johnson's leadership, the former minister told ITV's Robert Peston: "Regrettably, he appears to be a liability.
"And I think he either goes now, or he goes in three years' time at a general election."
At Prime Minister's Questions, Johnson attempted to assuage public outrage over claims he attended a "bring your own booze" party during the initial lockdown.
He confessed that he attended the 20 May 2020 gathering for approximately 25 minutes to "thank staff groups" for their efforts.
"I believed implicitly that this was a work event." he stated.
However, he added: "In retrospect, I should have escorted everyone back inside.
"I should have found some other way to thank them, and I should have recognized that - even if it could have been said technically to fall within the guidance - there would be millions and millions of people who simply would not see it that way."
Labor leader Sir Keir Starmer said Johnson's justification was "so ridiculous that it's actually offensive to the British public," and he urged him to "to do the decent thing and resign."
The SNP's Westminster leader, Ian Blackford, urged Tory MPs to force the PM out – and Lib Dem leader Sir Ed Davey agreed.
Sir Ed has written to the Met Police requesting that they investigate Johnson's attendance at the 20 May party.
Tory MPs reacted differently to the PM's comments, with some claiming he seemed genuinely sorry.
Dan Poulter, who is also a psychiatrist, said: "I am pleased that the prime minister has apologized, but it's not much consolation to those of us who cared for patients on the frontline of the NHS and saw them die of COVID."
Dominic Raab stated that the Prime Minister "given a very clear account" of what occurred and expressed regret for the "perception" of rule violation.
He stated that Sue Gray was investigating specific allegations regarding the 20 May party and that the prime minister would update the Commons once she was finished.
Michael Gove, the Secretary for Levelling-Up, also defended the PM during a meeting of the 1922 committee.
Gove told the BBC before the meeting of Tory backbenchers that while it was "right for the PM to apologize," it was also "important we all wait for Sue Gray's report to conclude."
Chancellor Rishi Sunak was unavailable for an interview due to a visit to a West country pharmaceutical firm.
However, on Wednesday evening, he tweeted that Johnson was "right to apologize" and that he agreed with the Prime Minister's appeal for "patience" as Gray concluded her probe.