They did not, however, report any progress over major sovereignty issues dividing them.
"Our relations are pervaded by trust... the era of tensions is over," said visiting Turkish Foreign Minister Abdullah Gul at a joint press conference with his Greek counterpart George Papandreou.
"Our relations are definitely in a different framework," Papandreou said.
"As proof of our important cooperation through a step-by-step approach, we have taken the recent decision to clear mines (along the border) and cancel (military) exercises in Cyprus," he said.
Both countries are also cooperating ahead of next year's Olympics in Athens, "from security to the passing of the Olympic flame through Istanbul," Papandreou said.
The two ministers also announced new deals to boost bilateral trade and tourism.
Athens and Ankara will sign an agreement in December to scrap double taxation for companies doing business in both countries.
They are also mooting a scheme to allow tourists brief crossings from the Turkish mainland to nearby Greek islands without visa requirements, Papandreou and Gul said.
But the two ministers did not report any progress regarding the major issues separating Greece and Turkey: sovereignty over parts of the Aegean and the ethnically divided island of Cyprus.
"The climate is good but we have not reached concrete results yet," Papandreou said about ongoing meetings between diplomats from both countries trying to iron out Greek-Turkish differences over the Aegean.
"The climate is good but we have not reached concrete results yet"
George Papandreou, Greek Foreign Minister
On the border issue, which has brought the two countries to the brink of war twice in the past, Gul had said upon his arrival that Ankara and Athens intended "to settle their disputes through negotiations".
Improved relations with Greece, a European Union member, is of particular importance for Turkey, which is seeking to join the 15-nation bloc.
Greece insists however that Turkey must resolve all bilateral disputes before it can start membership talks with the EU, which is set to evaluate Ankara's progress at the end of next year.
Many see the issue of Cyprus - which has been split since 1974 into a Turkish-run north and an ethnic Greek south - as a major obstacle to Ankara's hopes of starting accession talks.
Cyprus remains a bone of
contention between the two
The US State Department's special envoy on Cyprus Thomas Weston will meet Papandreou after Gul's departure on Wednesday.
The foreign ministers of Greece and Turkey - two NATO allies - have been meeting regularly since 1999, when relations began to thaw after two deadly earthquakes in both countries in the space of a month stirred mutual sympathy.
The two sides have signed more than a dozen accords on relatively uncontroversial issues.
But the diplomatic rapprochement has nonetheless caused frustration as it has yet to yield concrete results on the major issues separating the two sides, such as the delimitation of
airspace, maritime borders and the continental shelf under the Aegean Sea.
Gul will meet Greek Prime Minister Costas Simitis on Wednesday before leaving for Bosnia to attend the funeral of its former leader Alija Izetbegovic.