At least four rockets targeted the US Embassy in Baghdad's heavily fortified Green Zone on Thursday, two Iraqi security officials said.

The area is home to diplomatic missions and the seat of Iraq's government,

Three of the missiles struck within the perimeter of the American Embassy, the officials said.

Another hit a school located in a nearby residential complex.

The officials spoke on condition of anonymity because they were not authorized to talk to the media.

An Iraqi military statement said a girl and a woman were injured in the attack, without providing more details.

The statement said the rockets had been launched from the Dora neighborhood of Baghdad.

The US Embassy in Baghdad said in a statement that its compound had been attacked by "terrorists groups attempting to undermine Iraq's security, sovereignty, and international relations.”

The embassy's C-RAM defense system - supposed to detect and destroy incoming rockets, artillery and mortar shells - was heard during the attack.

The attack is the latest in a series of rocket and drone attacks that have targeted the American presence in Iraq since the start of the year, following the second anniversary of the US strike that killed Iranian Gen. Qassim Soleimani.

The US warned Iran on January 9 against harming any Americans, referring also to by Iran-backed militia forces in the region.