"It would be risky to say we are going to bring the treaty back to life when we are facing... the moment of truth," AFP news agency quoted Slovenian Foreign Minister Dimitrij Rupel as saying.
"I don't have any solution. We are going to listen to Minister [Micheal] Martin, maybe he has a solution. We are going to wait and think and let us respect the vote that has taken place."
EU foreign policy chief Javier Solana, quoted by AFP, promised that the EU would solve the problem, but added: "I don't know how we'll solve it practically."
Irish Prime Minister Brian Cowen has also said there is no obvious solution for a way forward on the Lisbon treaty, which is meant to streamline the workings of the EU and give it a stronger voice in the world.
Mr Sarkozy's Czech counterpart, Vaclav Klaus, whose signature is needed for the treaty's approval, has broken ranks by calling the Irish No a victory for liberty and reason over elitist plans and European bureaucracy.
There is also growing pressure on UK Prime Minister Gordon Brown to stop the treaty from going through the last stage of ratification on Wednesday.
Mr Brown made clear on Monday that he intended to press ahead with the ratification process, but stressed that the treaty could not come into force until all 27 members sign.
He added that a "short period of reflection" was needed for the Irish Republic to assess what proposals it might offer for resolving the situation.
Meanwhile, more federalist leaders like Luxembourg's Jean-Claude Juncker have revived calls for a multi-speed Europe.
They say that some countries could push forward with integration in what he called a Club of the Few.
The treaty is aimed at helping the EU to cope with its expansion into eastern Europe.
It provides for a streamlining of the European Commission, the removal of the national veto in more policy areas, a new president of the European Council and a strengthened foreign affairs post.
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