ABOARD A U.S. MILITARY AIRCRAFT — The top U.S. general in Europe is looking at options including moving a U.S. warship to the Black Sea and bolstering scheduled NATO exercises in response to Russia's annexation of Crimea, a U.S. defense official told Reuters on Tuesday.

A small team of about 10 soldiers from an Army brigade could also head to Europe "very soon" to better prepare for a larger scheduled deployment this summer as part of a NATO response force.

"This brigade combat team was already scheduled to be part of the NATO response force going this summer. And we're just looking ... at ways that we can improve their deployment even more," the official said, speaking on condition of anonymity.

NATO said earlier on Tuesday it was suspending all practical cooperation with Russia in protest at its annexation of Crimea, and ordered military planners to draft measures to strengthen its defenses and reassure nervous Eastern European countries.

Gen. Philip Breedlove, who is both NATO's supreme allied commander Europe and the head of the U.S. military's European Command, was also "going to look at the full spate of upcoming NATO exercises" to see if there were ways they could be enhanced, the U.S. official said.

The United States deployed a warship to the Black Sea last month for exercises with allies. It also increased the number of U.S. aircraft in regular NATO air patrols over the Baltics and beefed up a previously planned training exercise with the Polish air force.

The United States also suspended all military engagements with Russia on March 3.