ODESSA, Ukraine—The U.S. is channeling support to Ukraine’s navy to help counter Russian efforts to choke its neighbor’s economy and destabilize its pro-Western government by blocking access to ports.

U.S. training and equipment have helped strengthen Ukraine’s army in its five-year conflict with Russia, but the fresh U.S. focus reflects concern over the Kremlin’s new maritime efforts to halt Ukraine’s westward integration and keep it in Russia’s sphere of influence.

Russia...