The Labour party is being warned not to "retreat into itself", as the battle rages over Tony Blair's refusal to name the day for his departure.
Mr Blair refuses to say exactly when he plans to step down
Minister Hilary Armstrong says the party needs to listen and engage with the public, and not resort to "tittle tattle" over the leadership transition.
A number of MPs have expressed concern that the lack of clarity is damaging their electoral prospects.
But the PM says the party should stop "obsessing" about when he will go.
Mr Blair is thought to have enraged Labour MPs by refusing to use this month's Labour conference to give an exit timetable.
Ms Armstrong, minister for social exclusion and a key Blair ally, conceded that the leadership transition was a "unique situation", but argued that the party had to get on with the job of working with the British people.
"The real test is for the party in how it handles the transition," she told Andrew Marr on the BBC's Sunday AM programme.
"But it should handle the transition knowing that it is no good us retreating into ourselves - we have got to be out there with the public understanding what their anxieties are right across the board.
"I am comfortable in a government that is driving forward, fulfilling its manifesto pledges and getting on, not with the tittle tattle, not with who's supporting this one or that one, but what are the issues that are challenging us."
Defence Secretary Des Browne, an ally of Chancellor Gordon Brown, said the party had to learn how to handle the transition process properly.
He told Sky News' Adam Boulton programme: "A prime minister that has served this country well in my view should be left to determine the time that he moves on himself.
"In my view the party will support Gordon Brown as the next prime minister."
Blairite Work and Pensions Secretary John Hutton urged his Cabinet colleagues "to move on from the constant speculation about when the prime minister will leave office".
The comments came as close allies of Mr Blair and Mr Brown continued the debate about the prime minister's future in Sunday's newspapers.
Ex-Transport Secretary Stephen Byers, a Blair supporter, told the Sunday Telegraph Mr Brown should outline Labour's future.
He said there was "both a challenge and an opportunity" for anyone who hoped to take over as party leader.
"They should use this period ahead to detail their vision and policies for the future and the political direction they want the Labour party to take," he said.
But Ed Balls, economic secretary to the Treasury and one of Mr Brown's closest allies, described a proposed policy debate before Mr Blair steps down as "absurd".
"I do not believe the Conservative party can win the next election. But we must make sure we do not lose it," he told the Observer.
"The idea that we need a period...of internal navel-gazing in which to renew is absurd."
The Sunday Times said ex-minister Alan Milburn was calling for others to challenge Mr Brown for the leadership.
Mr Milburn, another in the Blair camp, feared what he called a "headlong rush" to appoint a new leader.
Silence not golden?
He added that replacing Mr Blair would "not in itself renew Labour", and went on to say the debate should be open to all comers because there could be "no monopoly in wisdom".
"It is incumbent on all those with ambitions to lead (or deputy lead) the Labour party not just to throw their hats into the ring but to put ideas on the table," he said.
"A Trappist vow of silence will not work," he said.
Mr Blair has said he will step down before the next general election - with Mr Brown favourite to take over - but has not given a departure date.