The Turkish Prime Minister has arrived in Athens for a visit that many hope will lead to improved Turkish-Greek ties.
Recep Tayyip Erdogan was expected to discuss economic matters with his Greek counterpart, George Papandreou, including financial crisis management.
But cuts in defence spending is also said to be high on the agenda.
The two countries have had difficult relations over the future of Cyprus and other territorial matters.
But now both Ankara and Athens say they want to achieve the goal of demilitarising their region.
Greece, which is being helped in a European Union financial bailout, has been spending as much as 5.6 percent of its GDP on defence in recent years.
Turkey’s EU affairs minister has also said that “neither the people of Greece nor Turkey need new submarines or fighter jets”.