It appears unlikely that Gordon Brown will face a major contest for the Labour leadership when Tony Blair steps down, Tessa Jowell has said.
Mr Reid [right] has hinted he will not mount a challenge
He will take over without a challenge from a senior minister, the culture secretary predicted in a speech.
Home secretary John Reid said on Sunday Labour would not be fractured after Mr Blair goes - remarks that commentators are saying indicate he will not stand.
Any contest is likely to be between Mr Brown and one of two left-wing MPs.
When asked about the leadership contest on Sunday, Mr Reid said there would be unity in the Labour Party, up to and beyond this week's local elections.
While not completely ruling out a leadership bid, Mr Reid said the Labour Party would not be "fractured" once the prime minister resigned and there would be "a coming together of the Labour leadership".
He told BBC One's Sunday AM programme: "The election that matters to me is the election which places before the British people the choice between Conservatives and Labour."
Ms Jowell echoed those comments in a speech in London on Monday, saying it was time to bring an end to "tribalism" within New Labour, with no more so-called Blairites and Brownites.
She said: "I believe we should use this leadership change to open up a wider conversation with the people of Britain.
"But if we want them to listen to us, really listen to us, then we have to make some changes ourselves.
"We have to bring an end to tribalism in New Labour. So no more Blairites and Brownites.
"Too much of our present political approach - too much of our conversation and argument - has been focussed on personalities and a debate in code that reinforces that tribalism - leaving people in the real world, beyond Westminster, with no idea what's going on at times.
"We have to break the codes that have characterised our language in the past few months."
If there is only a challenge from a left-wing candidate, Tony Blair is expected to come out in support of Gordon Brown once the contest to replace him gets under way.
Last week Labour MPs Michael Meacher and John McDonnell - who had been planning separate leadership challenges - announced they were uniting in their bid to target Mr Brown.
They agreed one of them would withdraw, depending on the level of backing they had when Mr Blair steps down.