Gordon Brown has insisted he would "encourage" potential challengers for the Labour leadership to stand against him.
The Chancellor issued his invitation as former Home Secretary Charles Clarke held out the prospect that Mr Brown might have to defeat three serious candidates in a showdown for the top job.
Mr Brown told Sky News: "I've always said if people want to stand they should be free and encouraged to do so. That's a matter for them as individuals. Then, of course, in the ordinary course of events the Labour Party as a party will make its own decision."
He added: "Obviously, anybody who wants to put their name forward should feel free to do so. That's what democracy is about, that's what an election is about. It's up to them, it's not up to me to say whether people should stand."
In an article for the Mail on Sunday, Mr Clarke stressed that the Chancellor was not a certainty to win the contest and said he believed several challengers could garner enough support among MPs to reach a run-off.
"A week is famously a long time in politics," Mr Clarke wrote. "But as in the past, the week between Tony Blair's resignation and the close of nominations for the leadership will be the longest of all. Time and again, this short period has turned expectations upside down."
Mr Clarke, who has previously criticised Mr Brown as a control freak, has not ruled out taking a tilt at the top job, and Blairites have been encouraging Environment Secretary David Miliband to mount a challenge. Home Secretary John Reid's leadership intentions have also been the subject of intense speculation.
Two candidates from the left of the party - John McDonnell and Michael Meacher - have already declared, but Westminster watchers think they will struggle to achieve the 45 MPs' nominations required to enter the final vote.
Mr Clarke said he believed Mr Blair would announce he was standing down "a few days after" the local elections on May 3.
Tory leader David Cameron said it did not matter to him who succeeded Mr Blair but claimed Labour was searching for "a personality". He told BBC One's Sunday AM: "To me it doesn't matter whether it's Brown, Clarke, Reid or Miliband. They are all part of a Government that's completely lost its way."
