Turkey's Prime Minister Recep Tayyip Erdogan has arrived in Greece on the first official visit by a Turkish premier in 16 years.
Mr Erdogan is travelling with Turkish business leaders
Turkey's application to join the EU, trade and the future of Cyprus are likely to dominate talks.
Correspondents say both governments have worked hard to build on improved relations over the last five years.
Previously, Greece and Turkey had long maintained a suspicious and sometimes hostile relationship.
Mr Erdogan, who is travelling with a group of Turkish business leaders, left Athens airport directly for the villa of his Greek counterpart Costas Karamanlis in Rafina, near the Greek capital.
The two leaders and their wives were to hold a private dinner there before official talks on Friday.
"We wish to open a new page in our relations," Mr Karamanlis said in a written statement to Turkey's semi-official Anatolia news agency.
The BBC's Jonny Dymond in Istanbul says history weighs heavily on the relationship between Greece and Turkey.
But both countries' governments have worked hard to build upon a friendship that sprang out of the aid each gave the other during devastating earthquakes in 1999.
He says a sticking point is still the divided island of Cyprus, where the Greek-speaking Cypriots rejected a UN plan for reunification in a referendum on 24 April.
The divided island of Cyprus remains a thorny issue
One of the main reasons was the continued presence of Turkish troops on the Turkish Cypriot side.
There are also sharp disagreements between Greece and Turkey about air and territorial rights over the Aegean Sea, which separates the two states.
But diplomats on both sides are upbeat about Mr Erdogan's visit.
However, one unofficial part of the visit may cause controversy.
On Saturday Mr Erdogan will visit Thrace, in Eastern Greece - home to around 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.