The prime minister came under fire after declaring he would not bow to pressures to reveal when he would stand down at this month’s party conference in Manchester.
He used an interview in The Times to urge colleagues to stop “obsessing” about the leadership and concentrate on governing the country instead.
“I’ve said I won’t fight another election. I’ve also said, on the record, that I will give ample time to my successor,” he told the newspaper.
That should be enough for “anyone reasonable”, he added.
But his comments sparked a backlash, with MPs and union leaders accusing him of fuelling speculation further and damaging the party and the country.
They have raised the possibility that an open letter or delegation could be sent to Downing Street in the run up to the Manchester gathering.
Tony Woodley, head of the Transport and General Workers Union, said those close to Mr Blair should be warning him against repeating the mistakes of his forerunner Margaret Thatcher.
“They should be advising him not to get himself into a position as Thatcher did, when she did not understand when to go,” he told BBC News.
Former cabinet minister Andrew Smith — a close ally of Chancellor Gordon Brown — warned that continued uncertainty was “very damaging”.
“I am disappointed that the prime minister has chosen to put it in these terms and that he won’t say more and I think there will be widespread concern amongst the public, as well as amongst Labour Party members,” he told BBC Radio 4’s Today programme.
“I would have thought it’s clear to everyone that the debilitating uncertainty over the leadership can’t go on — it’s bad for the country, bad for the Government, bad for the Labour Party, and ultimately bad for Tony Blair himself.”
The depth of unrest was underlined by criticism from MPs outside the “usual suspects” of serial rebels.
Welsh MP Wayne David called on Mr Blair to name a date — and said it should be before crucial elections in Wales and Scotland next year.
Lyn Brown and Sarah McCarthy-Fry — both elected last year — said Mr Blair had brought the situation he was complaining about on himself.
Bookmakers William Hill say they have shortened the price of Mr Blair leaving office in 2007 from even money to 4/7.