Mr Annan had separate meetings in New York with the Cypriot President, Glafcos Clerides, and the Turkish Cypriot leader, Rauf Denktash.
Cyprus, long a source of tension between Greece and Turkey, has been divided since Turkey invaded the island in 1974, in response to a failed coup aimed at union with Greece.
Observers suggest there is little likelihood of a breakthrough before Turkey's general elections on 3 November.
Diplomats say Mr Annan plans to delay putting his draft peace plan on the table until mid-November, to avoid interfering in Turkish politics.
Mr Denktash had already made his position clear.
International pressure
"Only one point. If EU takes Cyprus as a member, talks are ended and Cyprus is divided forever. Thank you," he said on his way into the UN building.
The two sides have been under strong international pressure to work out a solution to the conflict - with no result so far.
There has been little movement on either side, despite UN-backed reunification talks that have been taking place all year.
The Greek Cypriot side says it wants a united Cypriot state, with separate Greek and Turkish regions.
The Turkish Cypriot leadership says it wants two separate entities, joined in a loose confederation, which would replace the present internationally recognised Republic of Cyprus.
Priority accession
Only Turkey recognises Mr Denktash's breakaway territory as a state.
Cyprus is one of up to 10 countries that could join the European Union by 2004.
On 12 December, EU leaders gather in Copenhagen to make a final decision on which countries to accept in this wave of enlargement.
Greece, which assumes the EU's rotating six-month presidency in January, says it wants to make Cypriot accession a priority.
But Turkey has warned it might annex the Turkish north if this happens.