To be included on the ballot paper, leadership candidates need support from at least 100 Conservative MPs.
Public endorsements mean Mr Sunak has surpassed this threshold – with 121 backers – and Mr Johnson’s allies claim he has the numbers required to run too.
However, the latest Sky News tally suggests just 56 MPs have confirmed they would support Mr Johnson’s campaign to be prime minister for the second time.
One of Mr Sunak’s supporters – Richard Holden – rejected claims that Mr Johnson had 100 MPs behind him, and said this number of public endorsements had not been made “because they don’t exist”.
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The only person who has thrown their hat into the ring, Commons Leader Penny Mordaunt, has received endorsements from 23 of her peers.
The current contest has been expedited following Liz Truss’s resignation as prime minister, and nominations for the ballot paper are due to close at 2pm tomorrow afternoon.
If all three candidates were to receive 100 backers, there would be a vote by MPs – with the winning two put forward to the party membership.
A vote would then take place, meaning the new leader would be chosen by Friday.
In a significant moment for Team Sunak, Kemi Badenoch threw her support behind the former chancellor after a string of big names had flocked to Mr Johnson.
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While she admitted that she had been a member of “the Boris Johnson fan club”, she warned the Tories are not “organising a popularity contest” – and the party is “not a vehicle for any one individual’s personal ambitions”.
Writing in The Sunday Times, Ms Badenoch said of her decision to endorse Mr Sunak: “Like any work colleagues, we had our disagreements, which I elaborated on when we were competitors in the same contest.
“Now it is imperative that I let people know the decisions he made that I knew were absolutely right.”
She also spoke of his attention to inflation and reining in of “unnecessary, wasteful spending”.
Meanwhile, former foreign secretary Dominic Raab said it is “difficult to see” how Mr Johnson could become prime minister again when he is “absorbed and distracted” by the issues surrounding partygate.
Speaking to Sky News, Mr Raab said he was “confident” Mr Sunak would run in the Tory leadership race and was the “standout candidate” among the field.
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