The UK government has reacted coolly to growing pressure from France and Germany to continue the process of ratifying the EU constitution.
There is speculation Mr Blair has given up on the treaty
Number 10 is urging other EU countries to wait until the 16 June summit before setting out their stance on the treaty.
Foreign Secretary Jack Straw is expected to say on Monday that the UK referendum will be shelved in the wake of French and Dutch "No" votes.
But the government denies reports that Tony Blair has "given up on Europe".
During talks in Berlin on Saturday night, French President Jacques Chirac and German Chancellor Gerhard Schroeder urged other EU countries to continue the ratification process.
They said EU leaders were under a legal obligation not to abandon the treaty.
A French spokesman said Britain would bear "great responsibility" for finding a way out of the crisis when it took over the rotating presidency of the EU on 1 July.
Downing Street expressed little surprise at the Franco-German initiative.
But it pointed out that President Chirac and Chancellor Schroeder represented the views of just two countries, in a Europe now expanded to 25.
BBC political correspondent Norman Smith said the government remained privately hopeful that other European countries, particularly those from eastern Europe, would back the British stance.
Some Sunday papers claim the government has given up on the treaty.
The Sunday Times quoted unnamed Westminster sources as saying Mr Blair was "determined to bury the constitution".
One said the constitution was "dead", and others that it would not be possible even to "cherry-pick" parts of it.
It says Mr Blair will push instead for only minor institutional tweaks to help make the European Union look more transparent.
The Sunday Telegraph goes further, and says Mr Blair has given up on Europe as an idea worth fighting for - and will focus on Africa instead.
EU supporter and senior Conservative politician Kenneth Clarke said the constitution was "over", blaming the "defeat" on the "weak leadership" of Mr Blair and his European counterparts.
"None of them have made the European case at all to their public - they've all played short-term national politics blaming Europe for anything that was embarrassing to them," he told BBC News.
"In this country people would think you were dotty if you went ahead with a referendum on a treaty which plainly is no more."
But Britain's EU commissioner Peter Mandelson believes the new challenge of the French and Dutch voters' rejection of the treaty will give Mr Blair another two to three years in office.
"I don't think that what's happened in Europe this week will have any direct impact whatsoever," he told ITV1's Jonathan Dimbleby programme.
"If anything, it gives him a fresh calling."