Turkey’s top diplomat has agreed with his Greek counterpart in Athens to keep dialogue moving forward with the goal of resolving longstanding issues that have brought the two countries to the brink of war in the past.

Foreign Minister Hakan Fidan embraced Greece’s George Gerapetritis after they met on Friday and released statements on outstanding issues. They both expressed willingness to work on understanding the other side better on “critical issues”.

“We must seize the historic opportunity ahead of us and make the positive climate between our countries permanent. We should transform our eternal neighbour into an eternal friend,” Fidan said at a joint news conference with Gerapetritis.

“I have no doubt that we can achieve this goal with a sincere and constructive approach,” he added.

Greece and Turkey each claim an area in the Aegean Sea reaching 11km (about 7 miles) from their coastlines. Greece says it has a right to expand this area to 22km (14 miles) under United Nations rules, but Turkey warns that could lead to conflict.

In the eastern Mediterranean, the dispute centres on exclusive economic zones, where oil and other resources can be drilled.

No agreement but positivity

Migrants and asylum seekers are also a major issue with the two countries working to manage them better together. Greece wants Turkey to clamp down more on smugglers.

On the Greek island of Samos, a camp made for up to 3,500 migrants and refugees is now holding more than 4,000 people, according to Christopher Wegener, a humanitarian worker with Doctors Without Borders, known by its French acronym MSF.

“The camp’s population has drastically increased since summer, and right now, we can see that people are sleeping even in common spaces like kitchens and classrooms,” he told Al Jazeera.

Videos sent by migrants from inside the camp show worn-out floorboards and unsanitary bathrooms.

“Every room had a bed for people. But right now, there are eight people inside the room, so we sleep on the ground,” Abdullah, a Samos camp resident who asked that his last name be withheld, told Al Jazeera.

Reporting from Athens, Al Jazeera’s John Psaropoulos said there was no agreement on the main issues but there was a positive vibe and discussions over what to include in an application to the International Court of Justice in The Hague to arbitrate.

“Greece recognises only the issue of the continental shelf boundary. Turkey wants territorial waters and other issues included as well,” he explained.

Vehbi Baysan, assistant professor at Ibn Haldun University in Turkey, said the issues date back a century but there is political will to resolve them now.

“We’re also talking about the energy channelling from Middle Eastern countries and then going to Greece and to Central Europe here as well as major issues like migration. It seems cooperation is absolutely necessary between the two countries, and now is the right time,” he told Al Jazeera.