Justice minister and Brexit campaigner Dominic Raab has ruled himself out of standing in any Conservative leadership contest.
Raab told BBC Question Time on Sunday evening: "I won’t be running."
"We are going to have a new prime minister and a new team in place in about three months. I am absolutely convinced that will need to be a broad-reaching team, not just some divisive Brexiter operation."
Raab added he was "not ideologically fixed" on the next Tory leader being a pro-Brexit campaigner.
David Cameron resigned as prime minister on Friday morning in the wake of the EU referendum result. He plans to stay in post until his successor is chosen.
Boris Johnson and home secretary Theresa May are seen as two of the frontrunners for the job.
Conservative minister Anna Soubry, who campaigned strongly for a 'Remain' vote, said the next Tory leader should be someone with "senior experience in national government".
She told Question Time: "I am not friends with Boris at the moment."
The result of the referendum has thrown Westminster into chaos, with both the Conservative Party and the Labour Party appearing rudderless.
Conservative international development secretary Justine Greening, who backed 'Remain', today said the Tory party should bypass the need for a leadership contest.
Writing on Conservative Home, she said Johnson and May should form a joint ticket to unify the party.
"A leadership contest now is not in the interests of our country. It will mean our party focuses inward – at the very time our country most needs us to focus outward," she said.
"A leadership contest now is not in the interests of our country. It will mean our party focuses inward – at the very time our country most needs us to focus outward."