LITOCHORO, Greece—Helicopters carrying U.S. and Greek troops landed in a field at the foot of Mount Olympus on a sunny morning late last month during a live-fire exercise in which the joint forces practiced recovering a downed pilot.

The training session is the latest sign that the U.S. military is expanding its presence in Greece, which U.S. Secretary of State Mike Pompeo recently called a “critical ally” in the region.

U.S. and Greek forces have been training together since October at a base in the nearby town of Volos. Last year, unarmed MQ-9 Reaper drones began operating out of Greece’s Larisa Air Force Base.

And the U.S. military has occasionally been using bases in Alexandroupolis and Araxos, according to U.S. and Greek officials. More U.S. port visits and training exercises are under discussion.

The U.S. Navy has shared the use of a naval base at Souda Bay on Crete since the 1950s. But U.S. and Greek diplomats say the two NATO allies are now closer than ever before.