Two mortar rounds hit the Green Zone in Baghdad on Saturday and two rockets slammed into a base housing US troops, security sources said, according to AFP.
The Green Zone is the high-security enclave where the US embassy is based.
The Iraqi military said that one projectile hit inside the zone, while another landed close to the enclave.
Sirens rang out at the US compound, sources there told AFP.
A pair of Katyusha rockets then hit the Balad airbase north of Baghdad, where American troops are based, security sources and the Iraqi military said.
Security sources there reported blaring sirens and said surveillance drones were sent above the base to locate the source of the rockets.
The incident comes amid increased tensions between the US and Iran.
The US military carried out the air strikes against the Kataib Hezbollah militia in response to the killing of a US civilian contractor in a Friday rocket attack on an Iraqi military base.
On Tuesday, Iraqi militants laid siege to the US Embassy in Baghdad, setting fires and smashing security cameras before forcing their way into the compound.
US President Donald Trump accused Iran of orchestrating the violent protest. Iran rejected the allegations.
Overnight Thursday, the US eliminated Qassem Soleimani, the head of the powerful Quds Force of the Iranian Revolutionary Guards Corps (IRGC) in a drone strike near the Baghdad International Airport.