Iranian warplanes have launched several airstrikes in recent days against Islamic State militants in eastern Iraq, U.S. and Iranian officials said Tuesday, the latest sign that America’s longtime adversary is conducting a parallel but largely unacknowledged military campaign in the conflict.

At least some of the bombing runs were by F-4 Phantom jets, American-built warplanes provided to Tehran before the 1979 Islamic Revolution that ousted Mohammed Reza Pahlavi, a close U.S. ally.

In the shifting political landscape of the latest Iraq war, Tehran and Washington are in effect aligned on the same side and are conducting dual but separate military operations to back the beleaguered Baghdad government. […]