A spokesperson for said reports that he is planning to stand down as Prime Minister on Monday in order to run again for Tory leader are completely untrue.
Mr Johnson resigned as leader of the on Thursday, but said he intends to remain in office until his successor is elected.
He said on Thursday: ‘It is clearly now the will of the parliamentary Conservative Party that there should be a new leader of that party and therefore a new prime minister.
‘And I’ve agreed with Sir Graham Brady, the chairman of our backbench MPs, that the process of choosing that new leader should begin now and the timetable will be announced next week.
‘And I’ve today appointed a Cabinet to serve, as I will, until a new leader is in place.’
But claims then emerged that Mr Johnson may be planning to run again, prompting Number 10 to clarify that Mr Johnson will stay out of the leadership race.
A spokesperson for Boris Johnson said reports that he is planning to stand down as Prime Minister on Monday in order to run again for Tory leader are completely untrue
Journalist Petronella Wyatt, Slot Online who had an affair with Mr Johnson when they both worked at the Spectator magazine, was among those who reported claims that the PM may attempt to stay in Downing Street.
She said: ‘A source at Number 10 tells me that Boris Johnson intends to stand down as Prime Minister on Monday, in order to run for the Tory leadership.’
Ms Wyatt had said earlier this week before Mr Johnson said he was stepping down that he would not resign.
She revealed a former Tory Minister telephoned her last night with the prediction that Boris would be gone by the end of the week.
But she said: ‘Knowing Boris as I well as I do, I could not concur.Boris’s obsession with his own divine right will tear apart his party and cause collateral damage to the country.’
Number 10’s insistence that the PM is definitely stepping down comes after new Education Secretary James Cleverly told Sky News ‘there is no such thing as a caretaker Prime Minister’.
Asked what he has resigned from, Mr Cleverly added: ‘He is resigning from his role as Prime Minister and leader of the party once a successor has been appointed.’
When presenter Kay Burley asked if that means the PM ‘hasn’t yet resigned’ from his role, Mr Cleverly added: ‘What I am saying is he has made an announcement, you can read it…’
Mr Johnson resigned as leader of the Conservative Party on Thursday, but said he intends to remain in office until his successor is elected.Above: Mr Johnson greeting his son Wilfred and wife Carrie Johnson after walking back into Number 10
Journalist Petronella Wyatt, who had an affair with Mr Johnson when they both worked at the Spectator magazine, was among those who reported claims that the PM may attempt to stay in Downing Street
So far, four Tory MPs have announced they are standing to replace Mr Johnson.
Former Chancellor Rishi Sunak has emerged as the frontrunner after launching his campaign with a slick video yesterday.
As well as Mr Sunak, former equalities minister Kemi Badenoch, Attorney General Suella Braverman and backbench MP Tom Tugendhat have confirmed they are running.
Defence Secretary Ben Wallace had been widely expected to launch his own bid but announced today that he will not take part in the race.
Mr Wallace said on Twitter: ‘After careful consideration and discussing with colleagues and family, I have taken the decision not to enter the contest for leadership of the Conservative Party.’
He added that it had not been an ‘easy’ choice to make, but said his focus is on his role as Defence Secretary and ‘keeping this great country safe’.
Other likely candidates, including Foreign Secretary Liz Truss and former Health Secretary Sajid Javid are yet to announce their bids.
Jeremy Hunt, who was Foreign Secretary and Health Secretary under Theresa May and David Cameron, has refused to comment on whether he will be launching his own bid.