The fighter appeared to be unarmed and never was in danger of coming in contact with the ship, said the officials. The passes, which occurred in the early evening there, ended without incident. A second Russian fighter jet flew at a higher altitude and was not a concern, said Warren.
A U.S. military official also said that a Russian Navy ship, a frigate, has been shadowing the U.S. warship, remaining within visual distance but not close enough to be unsafe. The official was not authorized to discuss the incident publicly so spoke on condition of anonymity.
Warren said that he is not aware of any official communication or protests by the U.S. to the Russians about incident.
The USS Donald Cook has been conducting routine operations in international waters east of Romania. The ship, which carries helicopters, was deployed to the Black Sea on April 10, in the wake of the Russian military takeover of Ukraine's Crimea region and ongoing unrest there. U.S. military officials have said the deployment is part of an effort to reassure allies and partners in the region.
Ukraine's acting President Oleksandr Turchynov on Monday called for the deployment of United Nations peacekeeping troops in the east of the country, where pro-Russian insurgents have occupied buildings in nearly 10 cities. The gunmen are demanding more autonomy from the central government and closer ties with Russia.
The West has accused Moscow of fomenting the unrest. And European Union foreign ministers are meeting in Luxembourg Monday to consider additional sanctions against Russian officials because of Moscow's annexation of Crimea.
The USS Donald Cook is now in port at Constanta, Romania.
Romanian President Traian Basescu visited the ship Monday and said a second U.S. Navy warship — a frigate from the Navy's Sixth Fleet in the Mediterranean Sea — is also heading to the Black Sea.
"My visit to the ship is symbolic, which first of all shows our respect to our NATO allies' reaction who have strengthened their presence in the Black Sea after Russia's annexation of Crimea," said Basescu, who is a former ship captain. He said the Russians "had created a circle of fire around the Black Sea."
The U.S. frigate, which has not yet been identified, is expected to arrive in the Black Sea in the next two weeks. According to a U.S. military official, the frigate is likely to replace the USS Donald Cook, which is expected to return to the Mediterranean Sea.
Associated Press writer Alison Mutler in Bucharest, Romania, contributed to this report.