The U.S. and Saudi Arabia have supplied Syrian rebel groups with a small number of advanced American antitank missiles for the first time in a pilot program that could lead to larger flows of sophisticated weaponry, people briefed on the effort said.

The new willingness to arm these rebels comes after the failure of U.S.-backed peace talks in January and recent regime gains on the battlefield. It also follows a reorganization of Western-backed fighters aimed at creating a more effective military force and increasing protection...