The European Union on Monday called on Turkey to avoid threats and "refrain from any actions that might damage good neighbourly" ties after Cyprus, a member of the bloc, accused the Turkish military of obstructing a ship exploring for gas.
Cyprus is one of several states, also including Israel and Lebanon, racing to tap gas deposits in the eastern Mediterranean.
Greek Cypriots run Cyprus's internationally recognised government, while Turkish Cypriots have a breakaway state in the north - recognised only by Ankara - and say resources around the island belong to them too.
After speaking to the Cyprus President Nicos Anastasiades, the chairman of EU leaders, Donald Tusk, said: "I call on Turkey to avoid threats or actions against any EU member and instead commit to good neighbourly relations, peaceful dispute settlement and respect for territorial sovereignty."
Turkey's foreign ministry, in a statement on Sunday, did not make any mention of obstructing the Eni ship but said the case was a unilateral move by Greek Cypriots that violated the sovereign rights of Turkish Cypriots.
It said the Greek Cypriots were jeopardising security and stability on the ethnically split island and in the region.
A spokeswoman for the EU's executive European Commission echoed Tusks's line by telling journalists on Monday: "Turkey needs to commit unequivocally to neighbourly relations and avoid any kind of source of friction, threat or action directed against a member state."
"The EU also stresses the need to respect the sovereignty of member states over their territorial sea and airspace," she added.
On Monday Greece accused Turkey of violating international law and said its "provocative conduct" was inconsistent with that of a country seeking accession to the EU.
"We call on Turkey to desist from further unlawful actions and to comply with its obligations stemming from international law," the foreign ministry in Athens said in a statement.
Relations between the EU and Turkey have become strained by disagreements over democracy and human rights, especially since a large-scale crackdown in the wake of a failed Turkish coup in 2016.
However, European countries still rely on Turkey as a NATO ally and as a brake to help reduce an influx of Syrian and other migrants and refugees into the bloc.
Turkey's EU minister, Omer Celik, will join 28 foreign ministers of the bloc for talks in Bulgaria on Friday. Ankara is pushing to lift visa requirements for its citizens travelling to Europe.
The EU is unwilling to grant Turks that concession now but, careful to avoid upsetting
President Tayyip Erdogan too much, is due to commit more money for the large number of Syrian refugees living in Turkey.
(Additional reporting by Samantha Koester and Karolina Tagaris, Writing by Gabriela Baczynska, editing by Gareth Jones, William Maclean)