The United States is co-hosting drills in the Black Sea with what is left of Ukraine's devastated navy, which lost about two thirds of its sailors and ships after Russia seized Crimea last year.

The maritime operation, dubbed Sea Breeze, began Tuesday and is an annual exercise that this year includes contingents from 11 countries practicing air defense, search-and-rescue procedures and a variety of other tactical maneuvers aimed at boosting regional security.

Ukraine's naval force was eviscerated when Russia seized the Black Sea peninsula of Crimea in March 2014. Moscow snatched much of the fleet moored in strategic ports, and convinced thousands of sailors to jump ship.

US Vice Admiral James Foggo III, who helped launch the international training mission, said on Wednesday that the Ukrainian navy dropped from about 17,000 to 5,000 sailors.

"They essentially lost about two-thirds of their people and about two-thirds of their ships," said Foggo, who had spent time in Odessa, which is the Ukraine fleet's new home after losing the Crimean port of Sebastopol.

"What they lost was capacity, they lost numbers," he told reporters. "But what they maintained was the professionalism of those who decided (to stay) with Ukraine."

Russian ships are asserting their presence in the Black Sea as the training exercise takes place, Foggo noted, but he said interactions between navies had so far not been tense.

The USS Donald Cook, a guided-missile destroyer, is participating in the exercises along with the Ukrainian frigate Getman Sagaidachniy, the flagship of Ukraine's navy that was only spared Russian capture by chance.

When Russian special forces soldiers without insignia started seizing strategic locations around Crimea, the frigate was on its way back home from a training mission in the Gulf of Aden.

Foggo met with Ukrainian Prime Minister Arseniy Yatsenyuk, and said authorities there are keen to modernize the navy.

"Perhaps bringing in some new warships as their budget will support," Foggo said. "Obviously they have to work through a number of issues."

Violence continues to simmer in eastern Ukraine, undermining ceasefire efforts.

Kiev and the West accuse Moscow of backing pro-Russia rebels with weapons and troops, a claim the Kremlin denies.

Other nations involved in the Sea Breeze exercise include Bulgaria, Germany, Greece, Italy, Moldova, Romania, Sweden, Turkey, and Britain.