LONDON (Guardian) -- Alan Milburn, the former health secretary and Blairite "outrider", reignited speculation on Sunday about the future of the Labour leadership as he refused to rule out challenging Gordon Brown for the role.

Asked whether he would challenge Brown, Milburn told the BBC's Sunday AM show: "That is a really good question and it deserves a really, really good answer. The answer is when we have a vacancy. At the moment there isn't a vacancy. I think personally it is highly unlikely, but that is a bridge that I think we all need to cross."

Brown's supporters attempted to play down Milburn's comments, with one describing it as a "solo mission". But another expressed annoyance that Blairites were saying the prime minister should continue while launching factional attacks on the chancellor.

The former health secretary is regarded as too experienced an operator to slip up in an interview, and colleagues asked why he had not closed down the issue.

"Alan should shut up," said a staunch Blairite. "I'm the kind of person he might hope would vote for him, but I just don't see any need for an alternative candidate to hold the torch of New Labour. If that's what he is thinking of, briefings and speeches against the Labour chancellor just do not seem fit." A minister said Milburn's comments were "completely baffling", adding: "It's extremely divisive at a time when we should be pulling together for local elections." Another said: "The two principals are surrounded by the equivalent of the knights in the cathedral. Every time Blair or Brown expresses some degree of exasperation they translate it as 'Who will rid me of this turbulent priest'." Like several colleagues, he dismissed Milburn's prospects as a candidate, adding: "He made a total dog's dinner of the general election campaign."

Arguments over the succession have reemerged after a period of calm, and gathered pace when Milburn and his close ally Stephen Byers criticized Brown's tax credit system in the Commons.

Relations became so poor that some Blairites reportedly believed Brown deliberately damaged Labour's chances on May 4 by withdrawing a £200 council tax discount for pensioners.

The joint appearance by the prime minister and chancellor at the party's local election launch was meant to end the speculation.

Milburn's comments infuriated the chancellor's supporters and senior party figures concerned that arguments about the succession were overshadowing the local election campaign.

They came as Roy Hattersley, a former deputy leader, said that in 50 years of membership he had "never known a time when the infighting in the Labour party was so bitter". He told the GMTV Sunday program that the uncertainty over the transition was causing immense damage: "The storms will go on until we know when the prime minister proposes to leave office."

A senior Labour source said No 10 believed the whole matter should be closed, with no discussion about when Tony Blair will stand down and whether Brown will face a contest. But many in the party now fear that is impossible.