NICOSIA (Reuters) - Cyprus's president said on Friday significant differences remained between Greek and Turkish Cypriots on the ethnically-split island but he hoped talks next week could resolve some outstanding issues.

Division along a U.N.-monitored ceasefire line has prevailed since a Turkish invasion in 1974 triggered by a brief coup inspired by the military then ruling Greece, and is a source of friction between NATO allies Greece and Turkey.

President Nicos Anastasiades, who leads the Greek Cypriot community, is due to take part in talks with his Turkish Cypriot counterpart Mustafa Akinci at a Swiss resort from Nov. 7-11.

The focus will be how to shift some boundaries now existing between the two sides as part of a comprehensive package of issues the sides need to resolve before a peace deal to unite the eastern Mediterranean island under a federal umbrella.

"Disagreements remain on issues which have been discussed. Important ... security and territorial issues - which are decisive - have not yet been the object of any substantive dialogue," Anastasiades told a news conference.

"It is known that on both issues there is a significant divergence in the positions of both sides."

Diplomats are cautiously optimistic that a solution could be in sight for the long-running conflict before the end of this year. A United Nations envoy this week said negotiations represented the best chance for a deal in decades.

Anastasiades and Akinci are both moderates leading their respective communities and the negotiations are directed toward reuniting Cyprus as a loose federation of two constituent, largely self-governing states.

In addition to territorial swaps, Greek Cypriots who represent Cyprus in the European Union are adamant that a deal see the withdrawal of Turkish forces from the island.

Thousands of Turkish troops are stationed in Cyprus's north, a breakaway Turkish Cypriot state recognized only by Ankara.

(Reporting By Michele Kambas; editing by Mark Heinrich)