Story highlights The USS Donald Cook will be in the Black Sea by Thursday

Russian troops are still massed on the Ukraine border

NATO representatives will meet April 15 to discuss the situation

The Navy warship USS Donald Cook is scheduled to enter the Black Sea no later than Thursday as part of the latest U.S. military effort to demonstrate support for Eastern European allies concerned about Russia's troop buildup along its border with Ukraine.

The movement of the guided missile destroyer was confirmed to CNN by two U.S. military officials who declined to be identified because a formal announcement has not been made. The ship will conduct exercises and port visits while in the Black Sea. The guided missile destroyer USS Truxtun took part in scheduled exercises in the Black Sea last month and departed March 21.

NATO members Bulgaria, Romania and Turkey have Black Sea coastlines, as do non-members Ukraine, Russia and Georgia.

The movement of the Navy warship into the Black Sea comes ahead of an April 15 meeting of top NATO political representatives to discuss and potentially approve a series of recommendations for additional military measures, including shortening the "response time" of NATO forces if there were a crisis. Other options on the table include more military exercises with member nations including the United States and potentially providing military advisers to Ukraine.

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Using classified and commercial satellite imagery, the United States estimates there are up to 40,000 Russian troops on the border with eastern Ukraine. Those troops remain positioned so close, and are so heavily armed, that the U.S. and NATO calculate they could "roll across" eastern Ukraine in three to five days, one official said. That's an estimate previously made by Gen. Philip Breedlove, the military chief of NATO. There has been no withdrawal of Russian forces; other than perhaps small numbers, so the estimate remains in place, the official said.

Washington also believes that the recent unrest in eastern Ukraine around the city of Donetsk is the work of "paid or compelled persons, heavily influenced by Russia," the official said. The U.S. assessment is that the Russians are looking for a provocation to move into Ukraine. But the Ukrainian military response of moving in methodically and arresting troublemakers worked in this case, the official said.