Ankara is at loggerheads with Greece and Cyprus over maritime hydrocarbon resources and naval spheres of influence, sparking fears of conflict.

"We remain deeply concerned by Turkey's ongoing operations surveying for natural resources in areas over which Greece and Cyprus assert jurisdiction over the eastern Mediterranean," Pompeo told reporters in Nicosia after a meeting with Republic of Cyprus President Nicos Anastasiades and Foreign Minister Nicos Christodoulides.

"Increased military tensions help no one but adversaries who would like to see division in transatlantic unity," he added.

"Regional corporation is absolutely necessary for durable energy security."

The Mediterranean island of Cyprus is divided between the internationally recognised Republic of Cyprus, a member of the EU, and a breakaway state set up after a Turkish invasion launched in 1974 in response to a coup sponsored by the military junta then ruling Greece.

Pompeo met the Cypriot officials after a trip to Doha where he inaugurated long-awaited talks between Afghanistan's government and the Taliban.

"Countries in the region need to resolve disagreements, including on security and energy resource and maritime issues diplomatically and peacefully," he said.

Pompeo said his trip to Cyprus would complement phone calls by President Donald Trump with his Turkish counterpart Recep Tayyip Erdogan and Greek Prime Minister Kyriakos Mitsotakis.

Anastasiades welcomed the US' "firm stance on condemning Turkey's illegal drillings within (Cyprus') Exclusive Economic Zone".

- Concerns over Russian warships -

Pompeo's "visit at a time when crucial developments are taking place in the Eastern Mediterranean, due to Turkey's illegal actions, aptly demonstrates the sincere concern and interest of the US in preserving stability in our region," he said.

Turkey's "unlawful activities... should be immediately terminated," he said, adding however that he conveyed Cyprus' support for resolving disputes in the eastern Mediterranean through dialogue.

Turkey, which is hunting for gas and oil reserves in waters claimed by fellow NATO member Greece, last month deployed an exploration vessel backed by military frigates.

Greece then responded by shadowing the Turkish ships and staging naval exercises with several EU allies and the United Arab Emirates in its own show of force.

Pompeo's trip comes shortly after the United States lifted a decades-old arms embargo on Cyprus, outraging Turkey, and days after Russian Foreign Minister Sergei Lavrov paid a visit to Cyprus.

Lavrov, who underscored Moscow's close relations with Cyprus, offered to play peacemaker in the region to ease tensions between Cyprus and Turkey in a dispute over maritime and energy rights.

Pompeo took the opportunity to remind Cyprus that Washington was uneasy about Russian warships stopping off at Cypriot ports.

"We know that all the Russian military vessels that stop in Cypriot ports are not conducting humanitarian missions in Syria and we ask Cyprus and the president to consider our concerns."

Nicosia has repeatedly stated it provides facilities to Russian warships based on humanitarian grounds.

Tensions rose in the region again when Turkey on Friday gave notice of a gunnery exercise off the coast of Sadrazamkoy in northern Cyprus between Saturday and Monday, despite the looming threat of EU sanctions.

Cyprus' Joint Rescue Coordination Centre -- attached to the defence ministry -- late Friday called Turkey's move "illegal" because it "violates the Republic of Cyprus' sovereignty and sovereign rights".

In a separate development, the Greek Cypriot National Guard said Saturday that it would take part in joint training manoeuvres with US forces and two boats.

"Two combatant craft medium transport vessels of the US special navy forces are in Cyprus to participate in joint military drills," it said in a statement.

The drills, which began Saturday and will last until September 20, are taking place in the "framework of the bilateral relations between the Republic of Cyprus and the US."