WASHINGTON—U.S.-backed forces operating in Syria have surrounded the eastern Syrian town of Shaddadi, considered a base of operations for Islamic State, Defense Secretary Ash Carter said Thursday.

Forces of the Syrian-Arab Coalition, or SAC, closed in on the town in recent days, Mr. Carter told members of a House Appropriations subcommittee. The coalition is a loose group of several thousand fighters who work closely with Kurdish forces in the region. The U.S. considered them highly motivated and has armed them repeatedly...