WASHINGTON — The White House cast doubt Friday on the Kremlin’s claims that thousands of troops massing on the border of southeastern Ukraine are merely involved in training exercises, deepening fears that Russian aggression will not end in Crimea.

“It’s not clear what that signals,” the national security adviser, Susan E. Rice, said to reporters in a briefing at the White House. But she added, “Obviously given their past practice and the gap between what they have said and what they have done, we are watching it with skepticism.”

At the Pentagon, senior officers and analysts said they were monitoring the Russian infantry, airborne, air defense and other reinforcements with growing alarm, uncertain of President Vladimir V. Putin’s ambitions.

Pentagon officials do not believe that a new Russian move into Ukraine is imminent. But one of their big worries is that American and NATO officials would have virtually no time to react if it did happen. All told, officials said, there are more than 20,000 troops near the border.