US Secretary of State Mike Pompeo on Tuesday backed talks between Greece and Turkey to resolve tensions in the eastern Mediterranean while announcing an enhanced US military presence in the region.

Turkey, Greece and Cyprus have been locked in a row over energy resources and maritime borders in the region, with Ankara infuriating the EU countries by sending research ships with naval escorts to work in contested waters.

Athens and Ankara have said they are ready to talk to try and solve the crisis.

"We strongly support dialogue between NATO allies Greece and Turkey and encourage them to resume discussion of these issues as soon as possible," Pompeo said after visiting a NATO base on the Greek island of Crete.

Pompeo said that the US navy's newest expeditionary sea base, the USS Hershel Williams, would from now on be based at the Souda Bay base on Crete, which he visited with Greek Prime Minister Kyriakos Mitsotakis.

"It's literally the perfect choice in light of the facility's strategic location. And it's symbolic of a defence partnership that will continue to expand and to grow," he said.

The 110-acre (44-hectare) Naval Support Activity base at Souda is the foremost US naval facility in the eastern Mediterranean.

Pompeo, on a European tour that includes stops in Italy and Croatia, also accused Russia of seeking to "destabilise the region, especially in Libya" and of peddling "disinformation on the (coronavirus) pandemic and trying to co-opt the Orthodox Church."

He also hit out at China, arguing that it "attempts to use economic power here and in the region to gain strategic leverage over European democracies."

Washington has previously urged Greece and Turkey to find "good solutions" to their dispute over territory and energy exploration rights.

European Council chief Charles Michel, meanwhile, warned that all options were still on the table to defend the interests of its member states if Turkey doesn't engage "constructively" in attempts to ease the dispute.

Mitsotakis on Tuesday said he hoped "exploratory talks" would start "soon", as well as parallel military de-escalation discussions within NATO.

"I'm reservedly optimistic that now is diplomacy's turn," said Mitsotakis, who is hosting Pompeo at his family home in Crete.

 - Military ties -

 Pompeo last October signed a defence agreement with Greek authorities allowing US forces a broader use of Greek military facilities.

Greece, which has announced fresh arms purchases from France during its most recent tensions with Turkey, intends to further upgrade the naval facilities at Souda for its own navy operations.

"Our country wants to make its presence felt in the eastern Mediterranean, and this will be done through the upgrade of Souda," Defence Minister Nikos Panagiotopoulos told parliament on Monday, according to Greek state agency ANA.

On Tuesday, Pompeo also called for an end to fighting between Armenian and Azerbaijani forces over the breakaway region of Nagorny Karabakh.

"Both sides must stop the violence and work with the Minsk group... to return to substantive negotiations as quickly as possible," Pompeo said, referring to the so-called Minsk Group of mediators that includes France, Russia and the United States.

On Wednesday, Pompeo will fly to Rome for meetings with Italian government and Vatican officials. He will subsequently visit Dubrovnik on Friday.