The Prime Minister was unmoved by repeated talks of a second vote of confidence. He just barely survived a vote of Conservative MPs last month, with the rules banning another 12-month vote.
But some in the party are urging the 1922 committee of backbench MPs to change the tide so that another vote of confidence can be held in the coming weeks.
A close ally of Mr. Johnson said any switch would “hold a gun to the head” of any future Tory leader.
They added: “They would never be able to get by with anything as they would be constantly exposed to the whims of MPs.”
Convinced of the backbench Tories will not move to really enforce a new vote, the prime minister seemed to be teasing those who have been planning against him in recent days.
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He told the BBC: “If you say you want me to undergo some kind of psychological transformation, I think our listeners will know it’s not going to happen.
“What you can do, and what the government needs to do, and what I want to do, is to keep changing and reforming and improving our systems and our economy.”
Today is the first day that Mr. Johnson has been in the UK for more than a week after attending a series of international summits.
Before his departure, allies of the party leader feared that his absence would be used to plan his downfall.
But after nine days out of the country, there was little progress in the planners’ efforts to oust their leader.
There is still a lack of consensus on whether to change the voting rules.
Former Brexit secretary-general David Davis, who has called for the prime minister to resign, said the change in the system would be “wrong” and said: “Rules are rules.”
He asked, “Do you want a leader, whoever it is, to look over his shoulder every month at this tax increase or whatever?”