Left-wing Labour MPs Michael Meacher and John McDonnell have delayed a decision over which one of them will run for party leader until Monday.
The backbenchers have said the candidate with the most backing from Labour MPs would go forward to challenge Chancellor Gordon Brown.
But they say the level of support for each was "too close to call" and more "clarification" was needed.
They say they jointly have the backing of enough MPs to mount a challenge.
Mr Meacher and Mr McDonnell are so far the only declared contenders to succeed Tony Blair, with Mr Brown - the clear favourite - due to launch his bid on Friday.
They have agreed to pool their support in the hope that between them they will get the backing of 45 Labour MPs needed to enter the leadership contest.
Their candidacy announcement had been due for 1600 BST on Thursday, hours after Tony Blair announced he would leave office on 27 June, but a further meeting will now be held on Monday.
The MPs issued a joint statement saying: "As agreed, the campaign teams for Michael Meacher and John McDonnell have met to assess the level of support for each candidate.
"The outcome is that the issue is too close to call at the moment and a number of clarifications need to be made.
"The good news for the Labour Party is that there is clearly sufficient support to ensure that a leadership candidate will come forward from the centre-left."
Mr McDonnell told BBC News: "Anything can happen. No-one had ever heard of David Cameron before the [Conservative] leadership election."
Brown as favourite
He added: "I think there's a real demand for change, to learn the lessons of the last 10 years and build on that, and learn from the mistakes."
Mr Brown is the overwhelming favourite to succeed Mr Blair, and has the backing of more than 200 Labour MPs.
Anyone who gets the 45 Labour MPs backing them can enter the contest, which takes about seven weeks.
The votes are split into thirds - with Labour MPs, peers and European MPs making up one third, with Labour Party members and trade unions having the rest of the votes.