Leaders of the Greek and Turkish communities on Cyprus sat down together today for the first time in five years to try to resolve the dispute that has divided their island for two decades.

"This is the handshake of the century," said Turkish Cypriot leader Rauf Denktash as he greeted President Spyros Kyprianou, the Greek Cypriot leader, in the conference room of the U.N. Security Council.

The climactic round of negotiations on the establishment of a federal republic of Cyprus that would reunite the two feuding communities began with a statement by U.N. Secretary General Javier Perez de Cuellar, whose intense three-month mediating effort laid the groundwork for a pact. "If you are determined to reach an agreement," he told them, "a unique chance now exists. If this moment is lost, it may not readily recur."

In the earlier talks, agreement was reached in principle on territorial adjustments, constitutional issues, and a mechanism for breaking deadlocks that may result from the veto powers granted to the Turkish Cypriot minority.

From the Greek Cypriot viewpoint, the major gaps that must be bridged are a timetable for the withdrawal of the 24,000 Turkish troops that have occupied the northern third of the island since 1974; an assurance that Turkey will not be able to justify any future invasion by being designated a "guarantor" of the agreement, and acceptance of the principle that all Cypriots will be free to move, settle or own property anywhere on the island.

The Turkish Cypriots have taken the position that no more commitments are necessary, and all that remains is the establishment of timetables for opening the international airport at Nicosia to the Turkish Cypriot community, for turning over to U.N. administration seven areas now under Turkish control that would be resettled by Greek Cypriots, and for the coming into effect of a transitional government.