He said 10 months of talks to prepare for the Nice summit - which will discuss reforms to enable the European Union to allow in new members - were "practically stalemated".
His gloomy assessment of the situation comes as summit host President Jacques Chirac of France is on a whistle-stop tour of EU countries to try to resolve outstanding issues.
Click here to see how an enlarged EU might look
Principal among these is disagreement over dropping national veto rights, to ease decision-making in an enlarged EU.
Mr Prodi said it was vital for the 15 member states to give up their right of veto on key areas.
Michel Barnier, the EU commissioner overseeing the reform process, said failure to do so would be a recipe for paralysis.
"If you have 30 countries, each with a right to veto decisions, the whole thing is going to grind to a halt," he said.
Voting rights
President Chirac is due to meet UK Prime Minister Tony Blair on Thursday, with indications that Britain will insist on keeping a veto over taxation policy.
The UK is one of a number of the larger EU member states which have been jealously guarding their right of veto on certain key issues.
The BBC diplomatic correspondent says another sticking point in negotiations which could block any deal is the big member states' demand for a greater say in decision-making to reflect the size of their populations.
Mr Chirac said on Wednesday that an overall reform package hinged on a deal to change the voting rules.
EU hopefuls
Reforms must be agreed by the EU's leaders if the bloc is to open its doors to the 12 candidates now negotiating entry terms.
These are Bulgaria, the Czech Republic, Cyprus, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Romania, Slovakia and Slovenia. A 13th, Turkey, is still to begin negotiating membership conditions.
Because of long and complicated membership talks, and the subsequent ratification procedure in the national legislatures and the European Parliament, even the most promising of the EU hopefuls do not expect to join before 2004.
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