Multiple rockets hit an Iraqi base hosting American troops near the US embassy early Sunday, the latest in a flurry of attacks against US assets in the country.

"The Coalition confirms small rockets impacted the Iraqi base hosting (coalition) troops in the International Zone... No casualties," said coalition spokesman Myles Caggins.

That base, known as Union III, is the headquarters for the US-led coalition, deployed in Iraq since 2014 to help local troops fight the Islamic State jihadist group.

Iraq's military said three Katyusha rockets hit inside the Green Zone, the high-security enclave where the US mission and Union III are located, as well as Iraqi government buildings, United Nations offices and other embassies.

A fourth rocket hit a logistics base in a different neighbourhood operated by the Hashed al-Shaabi, a military network officially incorporated into the Iraqi state, the Iraqi military said.

There was no immediate statement from the Hashed.

Strikes on assets of both the US and Hashed at the same time are unusual, as Washington has blamed hardline elements within the military network for repeated rocket attacks on American installations across Iraq.

Sunday's was the 19th attack since October to target either the embassy or the roughly 5,200 US troops stationed alongside local forces across Iraq.

In late December, a rocket attack on the northern Iraqi base of K1 left one US contractor dead and unleashed a dramatic series of events.

Washington responded with retaliatory strikes against Kataeb Hezbollah, a hardline Hashed faction in western Iraq.

Days later, an American drone strike in Baghdad killed top Iranian general Qasem Soleimani and his right-hand man, Hashed deputy chief Abu Mahdi al-Muhandis.

Hashed factions have vowed revenge for the pair's death but said they would prioritise a political objective first: the withdrawal of US troops from Iraq.

But the network includes a broad range of groups and some have appeared more willing to harass US troops militarily.

Sunday's attack came just hours after one of the Hashed's Iran-backed factions, Harakat al-Nujaba, announced a "countdown" to ousting American forces from the country.

A top leader within Nujaba, Nasr al-Shammary, tweeted a photograph of what he claimed was an American military vehicle, adding: "We are closer than you think."

Sunday's assault sent warning sirens blaring across the diplomatic compound, a US military source and a Western diplomat based nearby told AFP.

AFP's correspondents heard multiple strong explosions followed by aircraft circling near the Green Zone.