Mr Blair's sweeping cabinet reshuffle following Thursday's dismal poll results failed to silence calls for him to quit.
Rebel MPs have given him a three-month deadline in which to announce plans for a handover of power.
Urging renewal, finance minister Gordon Brown -- widely expected to be his successor -- said a "stable and orderly transition" of power was required and put the onus on Mr Blair to name the day for his departure.
Mr Blair has pledged not to stand for a fourth straight term in office at the next election, due by May 2010 at the latest.
But a growing band of Labour MPs want him to specify when he plans to step aside -- and soon.
Signatures gathered
The rebels are gathering signatures on a letter urging Mr Blair to lay out his succession plans by July.
Mr Brown is eager for the top job but refused to turn the screw on Mr Blair directly.
"We don't need outriders dictating the agenda," the Chancellor of the Exchequer told BBC television. "The vast majority of people want what Tony Blair wants himself, what he has said that he wants to achieve, and that is a stable and orderly transition."
Asked if he knew when Mr Blair was going to make way, Mr Brown said: "No. Tony Blair has said himself a year ago that he wishes to play his part in organising that stable and orderly transition.
"We don't actually know who's going to be leader of the Labour Party.
"I think people will look to him, and it's not essentially a matter for me, it's a matter for him and the Labour Party." Mr Brown stopped short of directly linking renewal with Mr Blair's exit.
He added: "I'm determined that in the next stage of my political career I make sure that New Labour broadens its coalition so that we have got a wider group of support."
A growing body of MPs feels a revamped Labour requires Mr Blair tendering his resignation. Some 50 rebels have signed up to a draft letter, published in The Sunday Telegraph, which demands a timetable for a "dignified, orderly and efficient" leadership transition to be set out by July.
"We therefore ask the NEC (Labour's National Executive Committee), in consultation with the prime minister, to lay out, no later than the end of the current parliamentary session, a clear timetable and procedure for the election of a new Labour Party leader," it said.
Loyalists warn off plotters
Mr Blair loyalist Stephen Byers, a former transport minister, said the plotting put a stable handover of power at risk.
"If we want to have an orderly transition, what we cannot have is the forced removal of Tony Blair as our leader," he told Sky News television. "And for those people who are organising a coup against him, they are playing a very dangerous game and they should stop."
New Home Secretary John Reid warned the plotters they were not going to win and risked taking Labour "into the wilderness".
"The whole thing has been generated by people who want to push Blair out, they want to stop the reform programme and they want to change direction back to Old Labour.
"That would be complete catastrophe for the Labour government and the Labour party," the tough-talking Blairite told BBC television.
However, key Brown ally Andrew Smith, a former pensions minister, told the domestic Press Association News Agency: "I am furious and the party will be furious about attempts to stifle or stop the discussion which needs to be had about a timetable for the orderly transition of leadership."
The prime minister would have to muster all his survival skills gleaned from nine years in office to win back the confidence of his Labour Party and the public, observers said.
Mr Blair has gone through two of his darkest weeks in office, marked by scandals, local election losses and a brutal cabinet reshuffle.
The ruthless and sweeping reshuffle, aimed at injecting life into the government, saw the prime minister sack his home secretary Charles Clarke, demote his foreign secretary Jack Straw and take powers off his deputy John Prescott. Other key ministerial posts were also juggled.
The enduring John Reid has been handed the tough job of home secretary, his ninth ministerial job in nine years. Margaret Beckett, considered a safe pair of hands, becomes the first female foreign secretary.
Political analysts likened Mr Blair's situation to that of former Conservative prime minister Margaret Thatcher, who was ousted by her MPs in 1990, part-way through her third term in office and six months after bad local election results.