U.S. diplomatic missions in Iraq’s capital and the southern oil hub of Basra appeared to be the target of rocket fire Saturday, a day after protesters torched the Iranian consulate in a show of anger against the entire political class and foreign interference.

Rockets were fired at Basra’s airport, which houses the U.S. consulate, but landed outside the exterior perimeter and caused no damage, according to Jihad Diwan, the head of media for Iraq’s Civil Aviation Authority. Earlier Saturday, rockets were also fired toward Baghdad’s...