Two Conservative MPs who have criticised Boris Johnson said they might run for the committee in charge of organising the party’s leadership contests.
The action comes after the party was defeated by the Lib Dems and Labour in by-elections in Tiverton, Honiton, and Wakefield.
Oliver Dowden, the party’s chairman, resigned after the results, stating that “someone must take responsibility.”
Although Mr Johnson acknowledged the outcomes were not “great,” he promised to “listen and learn.”
Even though 148 of his MPs voted to have the prime minister removed from office earlier this month, he survived.
According to the 1922 committee’s rules, Mr Johnson is immune to further criticism for a full year.
However, Andrew Bridgen, the MP for North West Leicestershire, has indicated he is willing to enter the fray and run for election to the committee’s executive.
Mr Johnson declared that he would concentrate on “delivering for the people of this country” after the by-election losses.
The prime minister stated in a statement on Friday that he “had to take that” and anticipated that his detractors would continue to “attack” him.
Speaking in Rwanda at a gathering of Commonwealth leaders, Mr Johnson predicted that he would face “difficult times ahead” and that people would “continue to bash me up.”
According to former Conservative leader Michael Howard, the new leadership would make the party and the nation “better off.”
Lord Howard suggested that cabinet members think about resignation and that party regulations be amended to permit a fresh vote of confidence in the prime minister.
Nadine Dorries, the culture secretary in the Cabinet, and Dominic Raab, the deputy prime minister, both endorsed Mr Johnson.
Sajid Javid, the health secretary, responded, “Boris Johnson is our leader, is the PM, and he will be bringing us into the next election,” when asked if he had complete faith in the prime minister to win the next election.