Turkish Cypriot leader Mustafa Akinci left on Tuesday morning for New York where he is due to meet UN Secretary-General Ban Ki-moon on Thursday.
Akinci is being accompanied by Turkish Cypriot negotiator Ozdil Nami and other aides.
Akinci is due back in Cyprus on June 7.
His next meeting with President Nicos Anastasides is due to focus on substantive issues, according to Foreign Minister Ioanis Kasoulides.
Kasoulides told CyBC on Tuesday that issues to be discussed included governance, and aspects of property. After that the leaders would tackle territory and security, he said.
Their negotiators, Nami and Andreas Mavroyiannis were listing the points where there were convergences, where there were small gaps and where the gaps were large, he added.
“This assessment will be put to the leaders of the two communities who will discuss it and give guidance to the negotiators on how to proceed,” he said.
Kasoulides said the two leaders were determined to discuss and negotiate on all issues.
On confidence building measures (CBM), Kasoulides said for now discussion would remain focused on low-level measures as agreed. Asked about opening Famagusta as a CBM, he said it would be discussed at a stage when it could produce tangible results.
For now, CBMs such as opening more crossing points would be the main focus. He said the proposed crossings at Dherynia and Lefka would be opened as soon as both sides completed technical works such as fixing the roads in both areas.
But the leaders had also expressed the political will for more crossing points to open, Kasoulides said.