UNITED NATIONS—Russia and China vetoed a U.N. Security Council resolution that would have threatened sanctions against Syria's leadership.

It was the third time Russia and China vetoed a resolution intended to pressure the regime of Syrian President Bashar al-Assad to leave power. The failure of the latest diplomacy points to a growing likelihood that Syria's fate will be decided by bloody clashes in the streets of the capital and not in the halls of the U.N.

The...