WASHINGTON—President Biden is directing the Pentagon to deploy more than 3,000 American troops to bolster the defense of European allies in the first major movement of U.S. forces in Russia’s military standoff with Ukraine, U.S. officials said.

Mr. Biden is sending roughly 2,000 troops from Fort Bragg, N.C., to Poland and Germany this week and repositioning about 1,000 troops that are part of a Germany-based infantry Stryker squadron to Romania, on the North Atlantic Treaty Organization’s eastern flank closest to Russia, the officials said.