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.

“The Russian forces are reinforcing and bulking up along the eastern Ukrainian border,” a Pentagon official said. “Our view is they’re preserving all their options, including going in, absolutely. If they choose to do that, we just wouldn’t have much warning.”

President Obama cited the troop movements on Thursday in announcing new sanctions against officials with ties to Mr. Putin and in opening the door to broader measures against key industrial sectors.