The United States on Monday called on Greece and Turkey to find "good solutions" to a tense Mediterranean territorial dispute after the NATO neighbours agreed to hold talks.

Greece and Turkey have spent weeks at loggerheads after Ankara sent exploration vessels into disputed, potentially resource-rich waters in a crisis that roped in other European powers and raised concern about a wider escalation.

"We hope the exploratory talks not only get kicked off right, but it's important that they're resolved in a way that delivers outcomes that each of the two nations find more than acceptable," said US Secretary of State Mike Pompeo on a two-day visit to Greece.

"It's not just talking, we need to get to good solutions," he added in an interview with Greek news agency ANA.

Pompeo is in Greece to de-escalate tensions in the eastern Mediterranean and boost tentative steps at dialogue between Athens and Ankara, who said last week they were ready to start talks.

US Secretary of State Mike Pompeo hopes to de-escalate tensions in the Mediterranean in Greece talks
US Secretary of State Mike Pompeo hopes to de-escalate tensions in the Mediterranean in Greece talks POOL / Giannis Papanikos

"Let's meet, let's talk and let's seek a mutually acceptable solution. Let's give diplomacy a chance," Greek PM Kyriakos Mitsotakis said on Friday to Turkish President Recep Tayyip Erdogan, in an address to the virtual UN General Assembly.

In a joint statement after talks in Thessaloniki in northern Greece, Pompeo and his Greek counterpart Nikos Dendias said rival claims to territory under the Mediterranean should be resolved "peacefully in accordance with international law."

Pompeo will fly to the Greek island of Crete on Tuesday and tour the NATO naval base of Souda Bay.

Mitsotakis -- who is hosting Pompeo at his family home in Crete -- wants closer military ties with the US.

Greek and American troops take part in a joint training exercise in Greece in February 2020
Greek and American troops take part in a joint training exercise in Greece in February 2020 AFP / Aris Messinis

The secretary of state last October signed a defence agreement allowing US forces a broader use of Greek military facilities.

On Monday, both sides said they intended to "further enhance their strategic defence and security partnership" in talks in Washington next year.

A key element of the October deal was the northern Greek port of Alexandroupolis, a Balkans and Black Sea gateway of strategic value to the US navy and NATO.

The US has been granted priority status to the port after paying roughly $2.3 million (2.0 million euros) to remove a sunken dredging barge that had blocked part of the harbour since 2010.

At the time, Greek officials said the Pentagon was expected to invest over $14 million on the Greek airbase of Larissa and around six million euros at Marathi, part of the Souda base.

Later in the week, Pompeo will go to Italy, the Vatican and Croatia.

In Rome, the secretary of state will discuss efforts by the Trump administration to deter its European allies from using equipment by Chinese manufacturer Huawei in developing their 5G networks.

The US accuses Huawei of being a tool for Chinese espionage.

Pompeo is also scheduled to attend a meeting at the Vatican on religious freedom, his human rights priority. There, too, he will warn of China's actions against minorities, including Muslims.

China