WASHINGTON—Whirlpool Corp. won crucial backing from a government panel in its bid to limit competition from foreign washing machine makers, giving the Trump administration another opportunity to invoke little-used powers to ramp up trade enforcement.

The U.S. International Trade Commission voted 4-0 Thursday to approve the petition from the Benton Harbor, Mich.-based manufacturer seeking broad protection in the American market from South Korean rivals Samsung Electronics Co. and LG Electronics Inc. The vote came under a trade...