Several rockets fell on Saturday inside Baghdad's heavily fortified Green Zone, its Jadriya neighbourhood, and the Balad air base housing U.S. troops, the Iraqi military said, adding that there were no deaths.
"Several rockets targeting Celebration Square and the Jadriya area in Baghdad, and the Balad air base in Salahuddin province, with no loss of life. Further details to come," the military said in a statement.
In Baghdad, mortar rounds on Saturday evening hit the Green Zone, the high-security enclave where the US embassy is based, security sources said.
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 US embassy in Baghdad as well as the 5,200 American troops stationed across the country have faced a spate of rocket attacks in recent months that Washington has blamed on Iran and its allies in Iraq.
One attack last month killed a US contractor working in northern Iraq, prompting retaliatory American air strikes that killed 25 hardline fighters close to Iran.
Tensions boiled over on Friday when the US struck Soleimani's convoy as it drove out of the airport and US diplomats and troops across Iraq had been bracing themselves for more rocket attacks.