The Mediterranean island has been divided since 1974, when Turkey occupied the northern third in response to a coup by an Athens-backed junta seeking to annex Cyprus to Greece.

The last attempt to find a solution with talks in Switzerland collapsed in 2017, and a new round of talks in Geneva broke up on Thursday without a breakthrough.

"There is no sense in sitting at the negotiations table under the old conditions and without the recognition of our equal sovereign status," Tatar said during a televised press conference in Geneva after the talks wrapped up.

Tatar said Turkish Cypriots would "absolutely" not abandon their position.

Turkish Foreign Minister Mevlut Cavusoglu said there was "no common ground to restart negotiations", echoing comments made earlier by UN Secretary-General Antonio Guterres.

But he added Turkey would support unofficial meetings that seek a way out of the impasse.

"We said there must be a new negotiations process between two states rather than two communities," Cavusoglu told reporters alongside Tatar.

Guterres led talks which began in Geneva on Tuesday and were attended by Greek Cypriot leader Nicos Anastasiades and Tatar.

The island's guarantor powers, Turkey, Greece and Britain, also attended the meeting.

Cavusoglu accused the Greek Cypriot side of failing to bring anything new to the table.

He also vowed Turkey "would not make concessions" on the northern third's "independence, sovereignty and equality" and would support Tatar's bid for a two-state solution.