Updated

U.N. Secretary-General Antonio Guterres is due to return to Cyprus peace talks to push rival sides closer to a deal after Turkey raised the ante Tuesday by insisting that it won't sign any agreement involving the withdrawal of all its troops from the ethnically divided Mediterranean island nation.

"This is serious business and (Guterres') role is important," Turkish Foreign Minister Mevlut told reporters at the Swiss resort of Crans-Montana where week-long talks to end Cyprus' 43-year ethnic divide are taking place.

The island's Greek Cypriot President Nicos Anastasiades said he's hopeful that there's enough progress over the next 24 hours to justify Guterres' return trip to Switzerland on Thursday.

"It'll become clear in the next days, hours even," Anastasiades said, adding that Turkish proposals deviated from parameters the Guterres put on negotiations last week to nudge them forward. "And we're talking about tangible progress, not theories or words."

This time, Guterres' personal touch looks to be crucial to bringing rival sides to the cusp of a long-elusive deal.

Word of the U.N. chief's return came hours after Cavusoglu made it clear that a peace accord would not include a specific, agreed-upon date by which all Turkish troops would have to be pulled out.

"There will be no sunset clause ... and Turkish troops will be staying on the island because this is the demand of the Turkish Cypriots," Cavusoglu said. "If there is anybody dreaming this, they have to wake up, there will be no sunset clause."

Turkey has kept more than 35,000 troops on Cyprus since 1974, when it invaded in the wake of a coup mounted by supporters of union with Greece. The minority Turkish Cypriots think their presence undergirds their security and want them to stay.

Cavusoglu has previously stated Turkey's opposition to a full troop withdrawal as part of a deal to unify the island as a federation between Greek Cypriots and Turkish Cypriots. But Tuesday's remarks appeared unequivocal, leaving no negotiating room for Greek Cypriots, who have been pushing for a full troop pull-out in order to remove what they see as a threat and a vestige of control from Ankara.

It's unclear what effect Cavusoglu's remarks had on talks between Greek Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci. In addition, Turkey, along with Cyprus' two other guarantors — Greece and Britain, the island's former colonial ruler — are deeply involved in the negotiations, especially on the pivotal issue of the island's future security.

"The Turkish Cypriots have been very clear at every meeting that they ... have security concerns," said Cavusoglu.

However, Cavusoglu indicated there was room to change the security regime that operated before the 1974 invasion. He said the military intervention rights and security guarantees accorded to Cyprus' "guarantors" under the island's 1960 constitution could be adapted for the current day.

But he repeated that complete abolition of those intervention rights and security guarantees is a "non-starter" for both Turkey and the breakaway Turkish Cypriots.

Anastasiades has proposed an international police force, backed by the U.N. Security Council, to keep the peace once the island is reunified. He said outside military forces have no place on Cyprus, arguing that European Union statutes guarantee ample security.

Cyprus is an EU member, but only the Greek Cypriot southern part that is the seat of the island's internationally recognized government enjoys full benefits.

Akinci rebuffed Anastasiades' charge that the Turkish side's security proposals went astray of the framework that the U.N. chief had laid out.

Apart from security, a number of issues — including a Turkish Cypriot demand to take turns holding the federal presidency with Greek Cypriots — remain to be resolved in parallel negotiations.

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Associated Press Writer Suzan Fraser in Ankara contributed to this report.