The Pentagon on Friday estimated as many as 20,000 Russian troops may be in Crimea but acknowledged its information was imperfect, as U.S. Defense Secretary Chuck Hagel praised the restraint of Ukrainian forces.
Russian President Vladimir Putin denies that the forces with no national insignia that are surrounding Ukrainian troops in their bases are under Moscow's command. The West has ridiculed his assertion.
Pentagon spokesman Rear Admiral John Kirby, asked about the number of Russian forces in Crimea, cited estimates of up to around 20,000 of them. Pressed on the 20,000 figure, Kirby said: "That's a good estimate right now."
"But it's just an estimate. And as I said, we don't have perfect visibility on the numbers," Kirby said at a Pentagon news conference.
Ukraine's border guards have put the figure far higher.
Serhiy Astakhov, an aide to the border guards' commander, said 30,000 Russian soldiers were now in Crimea, compared with the 11,000 permanently based with the Russian Black Sea fleet in the port of Sevastopol before the crisis.
In a telephone conversation with Ukraine's Defense Minister Ihor Tenyukh on Friday, Hagel praised Ukraine's armed forces for not allowing the situation to escalate, Kirby said.
"(Hagel) stressed the firm commitment of the United States to support the Ukrainian people and to the sovereignty and territorial integrity of Ukraine," Kirby said.
The United States has shown no interest in pursuing military options in the dispute with Russia over the Crimea, but it has taken other actions, such as cutting off military exchanges with Russia on Monday.
The United State has also moved to reassure NATO allies, sending six more F-15 fighter jets this week to NATO's policing mission over the Baltic states of Estonia, Latvia and Lithuania.
Poland on Thursday announced the U.S. military would send 12 F-16 fighter jets and 300 service personnel to Poland next week for a training exercise.
Kirby stopped short of confirming those figures, saying the U.S. military was still working through details.
"No decisions have been made yet, and soon as we have a mutual decision between us and Polish authorities ... of course, we'll make that public," Kirby said.