At least 50 British MPs are thought to have signed a letter calling on the prime minister to set a date for his departure by the summer.
Speculation as to when exactly Tony Blair will step aside had reached fever pitch even before Labour’s woeful showing in Thursday’s local elections.
Nineteen months ago Blair said he would quit at some stage during this parliament, with Finance Minister Gordon Brown tipped to take over.
Brown says he wants to see a “stable and orderly” transition of power and admits Labour needs to take a good look at itself.
He said: “That is a process of renewal, exactly similar to the process before 1997, it’s a process of renewal that each party in a generation has to undergo.
“What we’ve had is a warning signal, a wake-up call if you like, a signal that cannot be ignored and that makes it more urgent we do what we’ve got to do and that is to renew ourselves to deal with these challenges ahead.”
According to newspaper reports, some 50 backbenchers and former ministers are to give Blair until the end of July to finalise plans for his departure.
MPs need 70 signatures to trigger a leadership contest.
The letter apparently urges the party’s ruling body to step in if Blair refuses to reveal a timetable.