Boris Johnson is defying calls to resign, as he attempts to face down a growing mutiny among his cabinet, BBC reported.
Home Secretary Priti Patel, a former close ally, has joined a group of rebel ministers who are urging the PM to stand down.
But he has defied the growing calls for him to quit, saying it would not be "responsible" for him to go.
Levelling Up Secretary Michael Gove has been fired from his cabinet, after he urged the PM to resign.
Mr Johnson earlier told senior MPs it would not be right for him to "walk away" amid economic pressures and the war in Ukraine.
Under repeated questioning by the Commons Liaison Committee, he ruled out calling a snap general election, saying the earliest date he can see for one is 2024.
A Downing Street source rejected speculation the PM would announce his resignation in Downing Street later.
"There is no lectern outside No 10 tonight. The PM fights on," the source told BBC News.
The ministers urging him to quit also include Chief Whip Chris Heaton-Harris, Transport Secretary Grant Shapps, and Welsh Secretary Simon Hart, according to BBC.
Mr Gove told him to go earlier, and Business Secretary Kwasi Kwarteng has told the chief whip the PM should resign.
Mr Johnson rang Mr Gove on Wednesday evening to tell him he was sacked.
A No 10 source said: "You can't have a snake who is not with you on any of the big arguments who then gleefully tells the press the leader has to go."
Mr Hart later resigned from his post, saying he wanted to help Mr Johnson "turn the ship around" but "we have passed the point where this is possible".
BBC political editor Chris Mason said the rebel group was joined in Downing Street by another set of ministers arguing he should stay.
The BBC has also been told Mr Johnson has been stressing that "millions" voted for him, and questioning whether any of his would-be successors would be able to "replicate his electoral success at the next election".
Meanwhile, Tory party bosses on the executive of the backbench 1922 committee have postponed a decision on whether to change the rules governing a vote of confidence.
However, elections to replace the committee have been pulled forward and will now take place next week.
Mr Johnson survived such a vote last month, and under the rules as they currently stand he would be immune from another challenge for a year.
The crisis engulfing Mr Johnson's premiership began on Tuesday, following the dramatic resignations of Chancellor Rishi Sunak and Health Secretary Sajid Javid, BBC reported.
They quit within minutes of each other following a row over Mr Johnson's decision to appoint Chris Pincher deputy chief whip earlier this year.
Their departures have triggered a wave of further resignations, with one in five MPs in government roles quitting their posts.
A senior ally of the prime minister told the BBC: "It's now a question of how he exits," adding the situation was "not sustainable".
