Greek PM Costas Karamanlis has called for past difficulties with Turkey to be put aside, on the first visit to Ankara by a Greek leader in almost 50 years.
The two leaders were not clear how they would proceed on major issues
The three-day visit is the most significant attempt to improve relations between the two countries.
Although few signs of progress emerged on major issues, especially Cyprus, the leaders said ties were strengthened.
Mr Karamanlis added that Greece wanted to see Turkey as a member of the EU once it had met its EU obligations.
Specific results were not expected from the visit, but correspondents describe it as a public commitment to keep talking.
'Look to the future'
Mr Karamanlis's meeting with Turkish Prime Minister Recep Tayyip Erdogan lasted over an hour longer than planned, and their news conference was also unusually lengthy.
Both men stressed the recent improvement in relations after years of mutual suspicion and hostility.
"I am here to show Greece's desire, which is to go beyond the difficulties of the past and to look towards the future with hope," Mr Karamanlis said.
Mr Erdogan said he thought the new year would present "new opportunities" for the two countries.
They spoke of new ties on the economic, cultural and military fronts, but there was little sign of progress on the main political problems that divide them.
Mr Erdogan called for Greek support to restart talks on the unification of Cyprus.
He said ending territorial disputes in the Aegean Sea - which brought the two countries to the brink of war just over a decade ago - must be a priority.
Mr Karamanlis called on Turkey to abide by international law in the Aegean and said that although Greece supported Turkey's ambitions to join the EU, it had many obligations to meet to make that possible.
"Provided Turkey continues on the reform path and meets criteria... Europe must accept it as a full member of the European family," he said.
After years of mutual suspicion, at times turning into outright hostility, relations between Greece and Turkey have improved immensely in the past decade, says the BBC's Sarah Rainsford in Istanbul.
The two nations have opened a joint gas pipeline and trade relations have boomed.