ATHENS — Germany's foreign minister was visiting Greece and Turkey on Tuesday in an effort to ease increasing tension between the two neighbors, which are at loggerheads over prospecting rights in the eastern Mediterranean.

Heiko Maas’s visit comes as Greece begins a military exercise involving its navy and air force in the Mediterranean southeast of Crete and south of the Greek island of Kastellorizo, near an area where Turkey has sent research vessel Oruc Reis, accompanied by warships, to survey the seabed for gas and oil deposits.

In response to the Oruc Reis’s operations, Greece put its armed forces on alert and sent warships to shadow the Turkish vessels.

Turkey’s Defense Ministry said Turkish and allied navy ships would be conducting “maritime training” in the eastern Mediterranean on Tuesday “to promote coordination and interoperability.” A Turkish official said the training would last for a few hours only. It wasn't immediately clear which countries were participating. Turkish media reported the exercise would be conducted south of the Greek island of Crete.

“Turkey and Greece are our NATO allies. There can only be solutions for the disputed questions surrounding the gas deposits in the eastern Mediterranean on the basis of international law and in sincere dialogue,” Maas said before his visit to the two countries.

“The tensions are not just weighing on the relationship between the EU and Turkey. A further escalation can only damage all sides, but above all those immediately involved on the spot.”

Greece says the area in which the Oruc Reis has been operating overlaps its own continental shelf and has demanded Turkey withdraw the ship. Ankara responded by extending its notification to shipping, known as a Navtex, about the research vessel’s operations to Aug. 27.

Athens retorted by declaring it will carry out a three-day military exercise in the area. Turkish President Recep Tayyip Erdogan warned that “as of now, Greece will be the only one responsible for any negative development in the region,” and said the military exercise “endangers the coastal and navigational safety of all ships in the region.”

The escalating tension has raised concerns of potential conflict between the two regional rivals, which have come to the brink of war three times since the mid-1970s, including once over prospecting rights in the Aegean Sea.

Greek Prime Minister Kyriakos Mitsotakis has warned of the danger of an accident when so many military vessels are concentrated in a small area at sea. Earlier this month, Athens said a Greek frigate and a Turkish frigate collided while shadowing the Oruc Reis. No injuries were reported on either side. Greek media reported the Turkish frigate had suffered minor damage above the waterline.

“The windows for dialogue between Greece and Turkey must now be opened further and not closed,” Maas said. “For this, instead of new provocations, we finally need steps toward de-escalation and a start to direct talks.”

Maas’ trip comes ahead of a meeting of EU foreign ministers in Berlin later this week, at which Turkey will be discussed. Maas noted that “Greece’s voice will have particular weight.”

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By ELENA BECATOROS and GEIR MOULSON Associated Press

Geir Moulson reported from Berlin. Suzan Fraser in Ankara, Turkey, contributed to this report.