The talks are a last-minute attempt at reuniting the Mediterranean island before it joins the European Union.
But neither Turkish Cypriot leader Rauf Denktash nor newly-elected Cypriot President Tassos Papadopoulos is happy with the plan.
The Turkish Cypriots still believe they are being asked to cede too much land, and the Greek Cypriots say not enough refugees are being given the right to return to their former homes.
Mr Annan began the day holding separate talks with the two men. Joint talks are expected later on Monday.
He has continued to warn both leaders that this is their last chance for a settlement.
"Decision time has arrived," Mr Annan wrote in an article in the International Herald Tribune.
"The choice is not between my plan and a radically different one. The real choice is between my plan and no solution at all."
Failure to agree, he said, would further entrench the island's divisions and harm Turkey's "European aspirations".
This would pave the way for Cyprus to join the EU next year as a united country.
If no agreement is reached, EU membership will apply, in effect, only to the southern, Greek Cypriot, part of the island.
The UN plan would create a Swiss-style federation of Greek and Turkish Cypriot constituent states.
Mr Denktash and Mr Papadopoulos want more time to negotiate, especially on the issue of the rights of refugees to reclaim their property.
Mr Denktash is under public pressure to agree to the UN plan, with growing numbers of Turkish Cypriots hoping for a boost to their economy through EU membership.
2. Wie is Kofi Annan?
3. In welke zee ligt Cyprus?
4. Welke twee bevolkingsgroepen leven er op Cyprus?
5. Wie zijn de leiders van die twee groepen?