Turkey has rejected a request from the European Commission to recognise Cyprus ahead of a key summit on Ankara's bid to open European Union accession talks.
Mr Barroso (right) says he supports Turkey's entry bid
Commission chief Jose Manuel Barroso stressed the importance of such a gesture when he met the Turkish prime minister on Friday.
But Recep Tayyip Erdogan said no steps would be taken before the summit.
Ankara does not recognise that the Greek Cypriot government represents Cyprus, which joined the EU in May.
The international community, on the other hand, does not recognise the Turkish Republic of Northern Cyprus (TRNC), where Turkey has around 35,000 troops.
At their meeting on Friday, Mr Barroso told Mr Erdogan that he personally supported Turkey's bid to join the EU.
But a Turkish official told the French news agency AFP: "Mr Erdogan rejected the appeal by Barroso concerning the recognition of the Republic of Cyprus by Turkey."
He said the Greek Cypriots did not deserve it after they rejected a United Nations plan for the unification of Cyprus, which Turkish Cypriots supported.
Mr Erdogan started his visited on Brussels on Thursday, ahead of the European leaders' summit on 16-17 December.
As he arrived to meet the Dutch prime minister, Mr Erdogan said he wanted a firm date for formal talks to start.
He said his country's aim was definite and unconditional membership.
Some EU countries say Turkey should be offered an alternative to full membership, if it fails to meet certain conditions set out by the bloc.
Some correspondents say the decision to start entry talks with Turkey could be the most important decision in the bloc's history.
But Mr Erdogan insists Turkey will not join "at any cost" and rejects the idea of a "privileged partnership" should membership negotiations fail.
"Our goal is definite, indisputable and unconditional membership," he told Turkey's Kanal D network before heading for Brussels. "We will tolerate no expression that might overshadow or dilute this."
"There is no reason for us not to be optimistic about the summit's outcome, but let me clearly state that 17 December is not doomsday for us."
The EU's Enlargement Commissioner Olli Rehn, who will also meet Mr Erdogan in Brussels, agrees.
He said Turkey already had a customs union agreement with the EU and was part of certain European crisis-management operations.
"In other words, Turkey already has a special relationship with the EU and therefore I have difficulties to see that would be an attractive option to anybody," he said.
"If you start accession negotiations, then the objective is accession, but it is open-ended in the way that we don't know if we achieve that, but we're working for that objective."
Dutch Prime Minister Jan Peter Balkenende, whose country currently holds the EU presidency, told reporters the EU nations wanted a "balanced, sustainable and consensual decision" about if and when to open entry talks.
He said Turkey had done well to meet the entry criteria, but added that "there are
some reservations and concerns about the implementation of laws banning torture, freedom of religion and the consequences for the labour market if Turkey becomes a member".
The BBC's Oana Lungescu, in Brussels, says the latest draft of the summit conclusions leaves it to EU leaders to decide on the date, process and outcome of negotiations with Turkey.
But it mentions the possibility of suspending negotiations at the initiative of the European Commission or on the request of EU member states, "in the case of a serious and persistent breach of the principles of liberty, democracy, respect for human rights and fundamental freedoms and the rule of law on which the Union is founded".
It also says Turkey should implement a zero-tolerance policy relating to torture and ill-treatment.
The draft also calls on Turkey to recognise Cyprus, an EU member since May, without explicitly mentioning it by name. Ankara only recognises the breakaway Turkish Republic in the north of the island and has refused any change of position before next week.