Backbencher Tom Tugendhat has become the first contender to throw his hat into the ring to succeed Boris Johnson.
The chairman of the Commons Foreign Affairs Committee, who has never served in government, said he would offer the party a "fresh start".
Attorney General Suella Braverman and arch-Brexiteer Steve Baker have both also indicated they will run - though before Mr Johnson's resignation.
Both ex-health secretary Sajid Javid and Transport Secretary Grant Shapps were understood to be seriously considering leadership bids, according to allies.
Writing in The Daily Telegraph, Mr Tugendhat said: "I am putting together a broad coalition of colleagues that will bring new energy and ideas to government and, finally, to bridge the Brexit divide that has dominated our recent history.
"I have served before - in the military, and now in Parliament. Now I hope to answer the call once again as prime minister. It's time for a clean start. It's time for renewal."
Mr Tugendhat appears to have support from the moderate wing of the Tory party with ex-Deputy PM Damian Green confirming hours earlier he was backing him.
Mr Green said: "I'm supporting Tom Tugendhat. We need a clean start, a fresh start, we need to get on with resetting the Conservative Party and resetting Government more widely in this country so that it gets back to being properly run, observing the conventions, supporting the institutions that we have in this country."
It comes after Attorney General Suella Braverman told ITV's Peston programme on Wednesday night she planned to run for PM.
The extraordinary move came as before Mr Johnson had even resigned.
"If there is a leadership contest, I will put my name into the ring," Ms Braverman said and called for Mr Johnson to go.
The move was highly unusual as Cabinet ministers usually quit if they no longer have faith in the prime minister.
But Ms Braverman said she had no plans to stand down from her role.
Meanwhile, MP Steve Baker revealed he was considering running in any leadership race, suggesting some individuals are “imploring” him to do so.
Pressed on his own ambitions, the Tory MP who worked in Theresa May’s government, told BBC Radio 4’s Today programme: “I have to think about it very seriously.
“As a working class kid from Cornwall I would never have imagined I’d seriously be on your programme, talking to you, about becoming prime minister.
“But the reality is some people I deeply respect are telling me, even imploring me, to do it. I must consider it seriously. The Conservative Home poll keeps putting me in the top 10 and I respect that."
