WASHINGTON—The Pentagon said Thursday that it carried out a rare flight over Ukraine under the international Open Skies Treaty to “reaffirm U.S. commitment to Ukraine" amid heightened Russia-Ukraine tensions.

It was the second such U.S. military gesture in two days after Russia last month shot at and seized three Ukrainian naval vessels and their crew members off Crimea. The U.S. Navy on Wednesday sent a warship through the Sea of Japan in a rare challenge to Russia’s maritime claims in international waters.

“Russia’s...