UNITED NATIONS—The United Nations Security Council rejected a Russian-backed resolution to condemn U.S.-led airstrikes in Syria Saturday, after a two-hour debate in which the U.S. said it was poised to strike again if the government of Bashar al-Assad repeats its use of chemical weapons.

Only Russia, China and Bolivia voted for the resolution, which called the airstrikes an aggression against Syria. Eight members opposed the resolution, including the U.S.and European allies on the council. Four members abstained.

The...