British media reported Labour members of parliament were circulating at least one letter calling for his resignation.
The majority of the 38 Labour MPs elected at the 2001 general election over the weekend drafted a letter calling for Mr Blair to step aside, The Guardian reported. The contents of the letter were being kept secret.
Mr Blair declined to set a specific date for his much-anticipated resignation in an interview with The Times published last week, though he has said he will step down before the next general election, due May 2010 at the latest.
An unnamed MP reportedly involved in the letter told the newspaper: "If the prime minister has decided that to set a timetable will undermine his authority, and his authority is already undermined, the obvious thing is for him to go now."
The BBC has also reported that at least three letters are circulating among Labour MPs calling for Mr Blair to step down, one of which says he should do so immediately.
Poll
News of the letters coincided with the publication of a Populus poll in The Times showing support for Labour fell while the opposition Conservatives held their ground.
Of the 1,504 people surveyed by Populus for The Times, 32 percent supported Labour, a two percentage point decline since July, while 36 percent declared support for the Conservatives.
The poll is the latest in a string of such surveys indicating support for Labour is dropping -- a YouGov poll published in The Daily Telegraph last month showed support for the Tories at 38 percent, with Labour at 31 percent.
Another poll, this time by ICM for The Guardian, on August 22 showed support for Labour falling to a 19-year low.
The Populus poll did have some positive news for Mr Blair, however -- just 30 percent of Labour voters want him to resign this year, while 40 percent want him to stay on until just before the next election.
Mr Blair faces more calls for him to set a date for his departure at Labour's party conference at the end of the month.