Former Cabinet minister Alan Milburn has refused to rule out standing in a contest for leader of the Labour Party after Tony Blair stands down.
Mr Milburn was health secretary from 1999 to 2003
Mr Milburn told BBC's Sunday AM programme that it was not yet an issue because there was not a vacancy.
He added it was "highly unlikely" he would stand, but it was "a bridge... we all need to cross" when the time comes.
Roy Hattersley on GMTV's Sunday Programme condemned tensions between the camps of Mr Blair and Gordon Brown.
The prime minister has said he will stand down before the next general election, without bowing to pressure to specify when.
Asked if he would run in a leadership contest, Mr Milburn said: "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."
Earlier, former deputy leader Mr Hattersley said Mr Blair and Mr Brown had "too much sense" to cause feuds, but that tensions between their rivals camps were "ruining the party".
Mr Hattersley said Mr Blair "must know too, that the forces behind him on the one hand and Gordon Brown on the other are going to continue to do the Labour Party appalling damage".
"I've been in the Labour Party 50 years and it's 40-odd since I was elected to Parliament - I've never known a time when the in-fighting in the Labour Party was so bitter."
He added: "One of the problems now, I have to say more on the Blair side than on the Brown side, is that many of the Blair supporters couldn't care a damn about the Labour Party.
"They care about their own faction, their own ideas, their own leader and that is corrosive for the party's interests."
There has been speculation about feuding between rival Labour camps
Mr Hattersley's intervention follows weeks of reports about renewed feuding between the two camps.
Mr Blair and Mr Brown put on a public show of unity last week at the launch of Labour's local election campaign.
But their refusal to answer any questions from journalists merely prompted further speculation about the rift.
Mr Hattersley said stories would continue until it was clear when the PM would step down.