Grant Shapps, the transport secretary, has become the latest Conservative to announce a bid to become the next prime minister.
Mr Shapps pledged to end “tactical government by an often distracted centre”.
He joins a leadership race that includes the former chancellor Rishi Sunak, who announced his bid on Friday, vowing to “restore trust, rebuild the economy and reunite the country”.
Mr Sunak resigned from the Treasury shortly after Sajid Javid quit as health secretary on Tuesday, prompting a wave of resignations that ultimately led to Mr Johnson’s downfall.
He has won the endorsement of a number of Conservative MPs, including former Tory chairman Oliver Dowden and ex-Cabinet minister Liam Fox.
Tories take sides as race to succeed Johnson gathers pace – politics live
Defence Secretary Ben Wallace was the bookies’ favourite to succeed Mr Johnson but announced on Saturday that he would not stand.
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Mr Wallace had emerged as the clear favourite in the latest YouGov poll of Conservative Party members – beating Mr Sunak, as well as Foreign Secretary Liz Truss and former defence secretary Penny Mordaunt who have yet to reveal whether they will stand for the leadership.
Tom Tugendhat, the veteran and chair of the foreign affairs select committee, became the first MP to announce he would run to be the new party leader on Thursday.
The former equalities minister Kemi Badenoch has also announced her intention to run, unveiling plans to radically cut the size of the state and preside over a “limited government focused on essentials”.
Mr Javid is understood to be weighing up whether to run for the leadership.
Dominic Raab, the deputy prime minister, is understood to have ruled himself out of the race for the top job, as has former levelling up secretary Michael Gove, who was sacked by Mr Johnson ahead of his own resignation.
Ex-health secretary Matt Hancock has also confirmed he will not run.
Mr Johnson’s government plunge into freefall after a series of scandals including partygate and, most recently, allegations against disgraced deputy chief whip Chris Pincher, which the prime minister initially denied knowledge of.
Mr Johnson announced his resignation in an address to the nation outside Downing Street on Thursday.
But it is unclear when he will leave Downing Street and has faced calls from some MPs to go immediately.