The U.S. military estimates some 12,000 Russian soldiers are supporting pro-Moscow separatists in eastern Ukraine.
U.S. Army Europe Commander Ben Hodges said the Russian forces are made up of military advisers, weapons operators and combat troops.
Hodges also said some 29,000 Russian troops are in Crimea, which unified with Russia last year.
Hodges said in Berlin on March 3 that helping Ukraine with weapons would increase the stakes for Russian President Vladimir Putin at home.
He added that "when mothers start seeing sons come home dead, when that price goes up, then that domestic support begins to shrink."
Russia denies aiding the rebels.
Hodges said what Ukraine wants "is intelligence, counterfire capability and something that can stop a Russian tank."
The White House still hasn't decided whether to send arms to Ukraine, and Hodges reiterated Washington wanted a diplomatic solution.