Tony Blair would be handing a "gift" to the opposition parties if he named the day for his departure, Education Secretary Alan Johnson has said.
Mr Blair is thought to have angered MPs by not saying when he will go
He argued it would be too soon for the prime minister to step down this year - but did not rule out standing for the top job himself.
Mr Johnson says there is no need for a "fundamental discussion of principles" about the direction of the party.
He spoke out after a number of MPs called for Labour to debate its future.
Mr Blair is thought to have enraged Labour MPs by refusing to use this month's party conference to give an exit timetable.
Instead he has told the party to stop "obsessing" about when he will go - following his decision not to stand for a fourth term.
Mr Johnson would not be drawn on when he thought Mr Blair should quit, but told BBC Radio 4's Today programme he thought this year was too early.
"I think it is a matter for the elected leader of the party," he said.
"He had a substantial majority in the general election just over a year ago.
"He has said he is not going to be there to lead us into the next election. He has said there will be an orderly transition. He has said he will do that in plenty of time.
"That is a reasonable proposition and I think the party will be scratching their heads. It's up to them who will become the next leader and deputy leader.
"They make that decision and I think they understand that actually saying the date when that decision would be made would be a gift to the opposition parties."
'Don't divide party'
Ex-Transport Secretary Stephen Byers has argued that Chancellor Gordon Brown - widely tipped to be Mr Blair's successor - 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.
Mr Johnson would not be drawn on his own leadership ambitions
But Mr Johnson said he believed the party would be looking at that proposal "askance".
"They know that divided political parties lose elections," he said. "The prime minister has made a very reasonable point.
"I don't think we need a fundamental debate about where the party is going. I think we had that in the eighties and early nineties.
"I agree with the renewal point, but I don't think there is any need for a fundamental discussion of principles about where we are going."
Mr Johnson was coy about his own ambitions for the party leadership, saying: "It's important that I carry on my work as secretary of state for education.
"I'm not going to be sidelined and diverted about that by talk about a possible election in the future."