Two mortar rounds hit the Iraqi capital's Green Zone on Saturday and two rockets slammed into an airbase housing US troops, security sources said, a day after a deadly American strike.

The precision drone strike outside the Baghdad airport on Friday killed Iranian commander Qasem Soleimani, top Iraqi paramilitary chief Abu Mahdi al-Muhandis and a clutch of other Iranian and Iraqi figures.

In Baghdad, mortar rounds on Saturday evening hit the Green Zone, the high-security enclave where the US embassy is based, security sources said.

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 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.