"No one can guarantee success in this," Finnish Foreign Minister Erkki Tuomioja told a press conference after a day of talks with his European Union counterparts, with relations with EU-hopeful Turkey high on the agenda.
They were still hoping for some movement ahead of an EU summit in mid-December.
"It is also quite possible that we cannot reach an agreement within this time but nevertheless we will continue with our support," said Tuomioja, whose country holds the EU's rotating presidency.
Many EU nations called for a swift recommendation by the European Commission on Turkey, EU sources said, with some seeking a freeze on some of the 35 accession chapters which any candidate nations must satisfactorily complete before joining.
Cypriot Foreign Minister George Lillikas said that a partial suspension of talks would be useless.
"We cannot agree to suspend relevant chapters as this is not a sanction and it has no relevant effect," Lillikas said after the talks, adding that the European Union could not be treated as "a menu a la carte".
"Turkey first closes the door, then they throw away the key and now they expect the European Union to break the door down," he added.
But nor did he agree, at the moment, on seeking a total suspension of the EU accession talks if Ankara does not make concessions in the coming weeks. "I cannot be optimistic" of any deal in the upcoming weeks, he said.
Finland, which has set out a compromise deal on Cyprus, has engaged to conclude their initiative before the end of November, he added.
Earlier, Enlargement Commissioner Olli Rehn said that Turkey would be allowed to enter the EU if it fulfilled all membership requirements, amid growing debate over Ankara's fitness to join the bloc.
"Yes, if Turkey meets all the conditions of accession in the end of this long and sometimes difficult journey, Turkey will become a member of the EU," said Rehn, during a debate in Brussels with Turkish negotiator Ali Babacan.
"If Turkey in 10 or 15 years is a modern European Turkey where all democratic values and the rule of law are respected, I am sure we can win the hearts and minds of the Europeans, succeed in the ratification process and even in (national) referenda," he said.
His comments came with public opinion in some EU quarters increasingly hostile to Turkey's membership ambitions, especially given its refusal to open its ports and airports to Cyprus.
A growing number of Turks are also growing sceptical that EU membership will ever be achieved.
"When we have issues like Cyprus on the table or when Turkish people see the anti-Turkish rhetoric in some member states, especially in some countries where elections are coming... the feeling of being not wanted is becoming more and more evident," said Babacan.
Turkey began often-tumultuous membership talks a year ago. Its accession process is expected to take at least a decade and no guarantees have been given that it will even be able to join at the end of it all.
A pause in EU relations would be wise unless Ankara swiftly lifts its embargo against Greek Cypriot ships and planes, Austrian Foreign Minister Ursula Plassnik told reporters as she arrived for the EU talks.
Turkey rejects any link between the Cyprus problem and its membership talks.
It refuses to open its air and sea ports to craft flying the flag of the internationally-recognised Cyprus Republic, whose Greek Cypriot government controls the south of the island, despite a customs deal with all EU members.

Copyright AFP (Agence France-Presse), 2006