A compromise candidate is now likely to emerge for the post of the president of the European Central Bank (ECB).
In what is likely to be a hectic two weeks of negotiations ahead of the May summit on the single currency neither the Dutch nor the French appear ready to stand down their candidates.
Mr Wim Kok, the Dutch Prime Minister, warned this week he would veto any French candidate for the post of head of the ECB, after Paris kept up its opposition to former Dutch central bank governor man Mr Will Duisenberg, who had been considered a shooin for the job.
France has its own candidate, Bank of France Governor Mr Jean-Claude Trichet, and has refused to drop him. "We can imagine a situation in which France would say that even if the rest of Europe is in favour of Duisenberg, he will not pass," Mr Kok declared on Dutch radio.
"Then we could say: `give them tit-for-tat'. The Netherlands or others, but certainly the Netherlands, can say: `Mr Trichet will not pass either'."
"If Duisenberg does not make it, I will not support any Frenchman. No way," Mr Kok warned. The French government reiterated its support for Mr Trichet following Mr Kok's outburst.
"Any third candidate must receive the support of all 11 countries likely to be joining the euro area," it said.
The ongoing row is beginning to prove embarrassing for EU states who are hoping to have a controversy free weeekend on May 1st and 2nd as they declare which sates will participate in the currency.
However, the French Prime Minister Mr Chirac said it was preferable but not essential that an agreed candidate be found by the May meeting. But a delay would hold up some key decision which can only be taken after a president is selected.
Mr Duisenberg, president of the forerunner of the ECB, the European Monetary Institute, looked certain to be chosen until Mr Chirac proposed Mr Trichet last November.
Since then a number of compromise have been proposed including a job-sharing agreement and positions in a number of other key EU institutions but none have been acceptable to both sides.
Most other EU states are understood to back Mr Duisenberg, particularly the Germans and, it is understood, the Irish. It is not clear which way the different countries would line up on compromise candidates.
One who has been regularly mentioned is Mr Jean Claude Junker the Luxembourg Prime Minister and Finance Minister.