The Cypriot Government has rejected a move towards a political settlement by the Turkish Cypriot leader, Rauf Denktash.
Many Turkish Cypriots have called for Denktash's resignation
Mr Denktash, who earlier this year turned down a UN peace plan, offered on Wednesday to return to Greek Cypriots the eastern town of Varosha.
The town, once one of Cyprus's main holiday resorts, has been deserted since partition in the 1970s.
But in a letter to Mr Denktash, the Cypriot President, Tassos Papadopoulos, said the UN plan, which includes more complex territorial arrangements, should be the main basis for negotiation.
The latest moves come just two weeks before Cyprus - in effect, the Greek-populated, southern part of the island - is due to sign a treaty of accession to the European Union.
Membership is to become effective next year.
Correspondents say the collapse of the UN initiative makes it highly unlikely that Cyprus will join the EU as a united country.
The UN plan would have created a Swiss-style federation of Greek and Turkish Cypriot constituent states.
Mr Denktash, in power since Turkey's 1974 invasion of Cyprus, opposed the UN plan primarily because it made no provision for his breakaway to achieve international recognition before the federation was formed.
Denktash: EU entry for the Greek side will complicate reunification
But his intransigence has been unpopular among ordinary Turkish Cypriots.
Tens of thousands of protesters have demanded his resignation, fearing they will fall further
behind the Greek Cypriot side economically if excluded from the EU.
The UN Security Council is expected to discuss Cyprus in the next few days, and Mr Papadopoulos said he hoped it would ask UN Secretary General Kofi Annan to continue his initiative.
Cyprus's accession in 2004 also will cause serious problems for Turkey if the island remains divided.
EU officials have warned that Turkey's own bid to join the EU will be jeopardised if it refuses to recognise a new member state.
Mr Denktash warned on Wednesday that Cyprus's entry into the EU as a divided island would complicate moves towards reunification.