German Chancellor Angela Merkel and French President Jacques Chirac have rejected the idea of setting a deadline for Turkey to comply with EU demands.
Mrs Merkel and Mr Chirac are co-ordinating positions on Turkey
Mrs Merkel, who takes over the EU presidency in January, said "We don't want to set any kind of ultimatum".
But the two leaders said the EU should issue a new progress report on Turkey's EU membership bid between next autumn and European elections in 2009.
Turkey's troubled bid will be on the agenda of an EU summit next week.
On Tuesday, Enlargement Commissioner Olli Rehn called on Ms Merkel and Mr Chirac to look for a "balanced solution" rather than calling for a strict deadline to be imposed on Turkey.
Earlier, a German government spokesman had said Mrs Merkel thought an 18-month deadline was an "appropriate and sensible instrument".
Mrs Merkel and Mr Chirac said they supported the European Commission's recommendation to partially suspend Turkey's accession talks.
The Commission is recommending the move because Ankara has failed to open its ports to ships from Cyprus, despite promising to do so in 2005.
Turkey says the EU should first fulfil a commitment to end the economic isolation of breakaway Turkish northern Cyprus, which is recognised only by Ankara.
Earlier, the Turkish Prime Minister, Recep Tayyip Erdogan, told Mrs Merkel that suspending talks would be "a grave mistake".
"Don't let this historic opportunity be hampered by the Greek Cypriot party with cheap tricks," he told her in a message quoted by Turkey's Anatolia news agency.
Greece also came out on Tuesday in favour of an 18-month deadline for Turkey.
EU foreign ministers will discuss the Commission's proposals at a meeting next Monday, and make recommendations to the EU summit on Thursday and Friday.
The French and German leaders were joined by Polish President Lech Kaczynski for informal talks in Mettlach, Germany, on Tuesday.