Mr Blair, known as “Teflon Tony” for his ability to withstand media storms and create the impression nothing will stick, has had one of the most bruising weeks in his nine years in power.
However, he vowed to forge ahead with market-inspired reforms, fighting “all the way” attempts by traditional Labour Party leftists to block them.
Speaking at his monthly press conference in London, he also confirmed that he saw ambitious Chancellor of the Exchequer Gordon Brown, the finance minister who has been waiting impatiently in the wings, as his obvious successor.
“To state a timetable now would simply paralyse the proper working of government, put at risk the necessary changes we’re making for Britain and therefore damage the country,” said the 53-year-old leader.
Mr Blair announced after Labour’s third election victory in May last year that he would serve a full third term in office but not run for a fourth when the next nationwide legislative vote takes place by 2010.
But poor local election results last week revived pressure within the party for a timetable for his departure and transition of power to Mr Brown.
Calls for Mr Blair to resign also came on Monday (local time) from David Cameron, the new leader of the main opposition Conservatives. The party scored well ahead of Labour in Thursday’s elections, a sign it is back in the running after years playing second fiddle to Labour.
“I think the sooner he goes the better, because I don’t see how his authority can recover,” Mr Cameron said.
The prime minister, who looked tired, confirmed Brown was his top choice to succeed him.
“Of course he is. When have I ever said anything different? That is why I suggest everyone calms down and lets us get on with the business of governing,” he said.
He said he was planning to tell a meeting of the Parliamentary Labour Party (PLP) – Labour lawmakers in parliament – he would stay on to fulfil his election mandate for reform in health, pension, schools, and justice.
He would tell them that for the sake of the nation’s interest he would honour pledges to ensure “a stable and orderly transition to a new leader” in the long run.
Leftists will turn back clock
Mr Blair warned that setting out an exit date now would be exploited by traditional leftists who seek to turn the tide against reforms undertaken by a party that he had steered toward the center with massive electoral success.
“That (leftist) way lies not a fourth-term victory but a defeat and a return to opposition, and I will fight that all the way,” said Mr Blair.
However, critics claim the whole party is distracted by the looming change in leadership, with members either still supporting Mr Blair or lining up behind Mr Brown.
Labour members said Mr Blair would be in for a rough ride at the meeting in which many are angry at his “ruthless” reshuffle of the cabinet in the wake of Thursday’s municipal council results, Labour’s worst since it took power in 1997.
The reshuffle, which followed ministerial scandals, saw the prime minister sack his home secretary, demote his foreign secretary, take powers off his deputy prime minister and juggle other key ministerial posts.
Mr Blair admitted the scandal surrounding his former home secretary Charles Clarke – whose department failed to deport hundreds of foreign prisoners once they were released – did “cause significant damage” to the party in the polls.
Analysts say Mr Blair swung the cabinet axe to demonstrate his authority, put the scandals of recent weeks behind him and give new purpose to his party, but the moves failed to quell calls for a clear handover of power.
Some 50 rebels have now 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.
A BBC radio survey of 104 Labour backbenchers found 52 who believed Blair should stand down within a year.