The message came as Turkish leaders said they would make no more concessions to the EU and would walk away if the 25-nation bloc offered anything short of full membership.
Ankara's July declaration refusing to recognise Cyprus had raised doubts about the start date, with France arguing it was inconceivable for Turkey to negotiate accession when it did not recognise one of the EU member states.
But Cyprus' foreign minister said on Friday he was hopeful Turkey's entry talks would go ahead and other ministers, meeting at a golf resort in Wales, said the message to Ankara would be that 3 October will be respected.
"Let me say that I am optimistic that they will start," said Cypriot Foreign Minister George Iacovou, when asked whether he shared British Foreign Secretary Jack Straw's confidence that the 3 October date for talks would be met.
Turkish Foreign Minister Abdullah Gul sparked new tension on Thursday by saying Ankara would not open its ports and airports to ships and planes from Cyprus, in apparent breach of its EU customs union that is a precursor to accession.
Gul was quoted on Friday by The Economist magazine as saying Turkey would walk away if the EU proposed new conditions.
"Now Turkey has nothing more to give (the EU). We have done everything related to the Copenhagen political criteria"
Turkish Prime Minister Tayyip Erdogan
EU Enlargement Commissioner Olli Rehn said full implementation of the customs union was "clearly a red line for the EU and is not a matter of negotiation".
Diplomats said France and Cyprus sought an EU commitment to suspend talks if Turkey failed to open its ports and airports to shipping and planes from Cyprus by next year, but other EU countries wanted to avoid any automatic suspension and review the issue again in 2006.
No more concessions
But Turkish Prime Minister Tayyip Erdogan said Turkey had no more concessions to make.
"Now Turkey has nothing more to give (the EU). We have done everything related to the Copenhagen political criteria," he told a gathering in the Italian city of Naples.
The Copenhagen criteria cover basic political freedoms and every EU candidate country must meet them before it can start accession talks.
Turkey refuses to recognise the internationally accepted Greek Cypriot administration and backs a breakaway Turkish Cypriot republic on the divided island.