Security sources in Iraq say two mortar rounds have hit Baghdad's Green Zone, while two rockets have hit a base housing US troops, just a day after a deadly American strike.

The precision drone strike outside the Baghdad airport yesterday 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 this 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.

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The US embassy in Baghdad, as well as over 5,200 American troops stationed across the country, has 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.

There has been no immediate claim of responsibility for this evening's attack.

With security worries rising after Friday's strike, NATO and a separate US-led mission suspended their programmes to train Iraqi security and armed forces, officials said.

"The safety of our personnel in Iraq is paramount. We continue to take all precautions necessary," acting NATO spokesman Dylan White said in a statement.

The US Embassy in Baghdad urged American citizens to leave Iraq.