Greek Prime Minister Costas Karamanlis has said he and his government will support Turkey's bid to join the EU.
Relations between Turkey and Greece have been improving
The announcement came during a landmark visit to Greece by Turkish Prime Minister Recep Tayyip Erdogan, the first of its kind in 16 years.
The EU is scheduled to make a decision at the end of the year on whether to begin accession talks with Ankara.
At a joint news conference on Friday, the Greek and Turkish leaders spoke of establishing a strategic partnership.
Mr Karamanlis said mutual relations had entered what he called a new orbit, reaffirming his support for Turkey's bid to enter the EU.
Analysts say Athens believes it would be in its own long term interest to have Turkey as an EU member.
Mr Karamanlis told the press conference: "We confirmed that the views of our two countries on the new road taken by Greek-Turkish relations coincide, and we noted
with satisfaction the progress made."
Mr Erdogan said he wanted the two countries to build a future together. He offered to provide any assistance requested by the Greek government in the final preparations for this summer's Olympic Games, which are struggling to meet deadlines.
"A rapprochement between Greece and Turkey began five years ago, and it continues very satisfactorily," he said. "Relations have acquired a directness, which is very important."
Mr Erdogan's visit is not expected to bring progress on the issue of Cyprus. Last month Greek Cypriots rejected a United Nations plan to reunify the island, whose Turkish and Greek communities remain divided.
But the fact that the vote did not affect relations between Athens and Ankara is significant, says the BBC's Athens correspondent Richard Galpin.
He says the trip has been highly symbolic, coming at what could have been a difficult time in relations between the two countries. He says the division of Cyprus is one of the most delicate issues between Greece and Turkey and the rejection of the UN plan could have triggered a crisis in relations.
On Saturday Mr Erdogan will visit Thrace, in eastern Greece - home to about 100,000 Turkish speakers, remnants of a population exchange in the 1920s.
Many of them call for their Turkish identity to be acknowledged, something Greece refuses to do.