WASHINGTON—The U.S. Defense Department has cleared the way for American military planes to start refueling Saudi Arabian jets bombing Houthi fighters in Yemen as the U.S. deepens its role in the expanding regional conflict, U.S. defense officials said Thursday.

U.S. Central Command is poised refuel Saudi planes when asked by Saudi forces, but the aerial refueling operations wouldn’t happen over Yemen, American military officials said.

...