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.

Greece and Turkey, both NATO members, have spent weeks at loggerheads after Ankara sent exploration vessels in August into potentially resource-rich waters claimed by both countries.

"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 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, who have agreed to continue exploratory talks interrupted in 2016, to find "good solutions” to their disputes over territory and energy exploration rights.

Mitsotakis on Tuesday said Athens was "ready for exploratory talks” which he hoped would start "soon”, as well as a 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.

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.