Pompeo met Greek Foreign Minister Nikos Dendias at a hotel in the northern city of Thessaloniki, as part of a two day trip to the country which will also include talks with Greek Prime Minister Kyriakos Mitsotakis.
"The United States welcomed Greece's confirmed readiness to engage with other countries in the region to achieve maritime delimitation agreements through dialogue and in accordance with international law," a joint statement released after the meeting said.
Tensions between Athens and Ankara flared last month after Ankara sent its Oruc Reis seismic survey ship into disputed waters in the eastern Mediterranean, escorted by gunboats, to map out sea territory for possible oil and gas drilling in an area thought to be rich in energy resources.
The two countries disagree over where their continental shelves extend, among a range of other issues.
Since then, Turkey has recalled the Oruc Reis, and Athens and Ankara announced last week they have agreed to restart exploratory talks, a move welcomed by the United States which has encouraged dialogue.
On Tuesday (September 29) Pompeo will hold talks with Mitsotakis at Souda military base, a NATO and Greek naval base, on the island of Crete.