It is the first such attack on the embassy in Baghdad since the start of the war in the Middle East, triggered by a joint US-Israeli attack on Iran, into which Iraq has been dragged.

Loud bangs were heard on Saturday night in Baghdad, AFP journalists said, with a witness near the fortified Green Zone, which houses the US embassy, reporting seeing air defences activated over the area.

"Four rockets were launched... toward the embassy," a security official said, adding that air defences intercepted three, while one fell in an open area in the embassy's airbase.

Two other security sources confirmed the attack, with one saying that all rockets were downed, including the one that fell in the airbase.

Prime Minister Mohammed Shia al-Sudani, ordered security forces to find the perpetrators of "the terrorist act" against the US embassy.

He said that "targeting diplomatic missions and embassies operating in Iraq is an act that cannot be justified or accepted under any circumstances."

Iraq, long a proxy battleground between the US and Iran, had said it did not want to be dragged into the conflict engulfing the Middle East, but it has not been spared.

It was drawn into the war from the outset, with strikes blamed on the United States and Israel targeting Iran-backed groups, which have since claimed attacks on US bases in Iraq and the region.

Drone and rocket attacks have targeted Baghdad International Airport, which houses a military base and a US diplomatic facility, as well as oil fields and facilities.

The northern autonomous Kurdistan region, which hosts US troops, has also been a main target of drone attacks that were largely intercepted.

Late on Saturday, an AFP journalist reported hearing the sound of a drone followed by at least three loud bangs in Kurdistan's capital Erbil, which also houses a major US consulate complex.

- Airstrikes -

On Saturday, airstrikes hit military bases belonging to the former paramilitary coalition Hashed al-Shaabi in the northern Nineveh province, the government's security media cell said.

One fighter was killed and three other wounded.

The Hashed al-Shaabi, or the Popular Mobilisation Forces (PMF), is an alliance of factions now integrated into the regular army, including several Iran-backed groups, which have a reputation for acting on their own.

Bases belonging to Hashed al-Shaabi have been hit several times since the start of the war.

The group's media cell said Saturday's strikes were carried out by "unidentified aircraft," but a PMF official told AFP that "an airstrike, likely American, hit a Hashed base" near the city of Mosul.

- Kurdish militants -

Iraq's Kurdistan also hosts camps and rear bases operated by several Iranian Kurdish rebel groups, which Iran has struck repeatedly since the start of the war.

Iran's Revolutionary Guards said Saturday they have targeted "separatist groups" in Iraqi Kurdistan, after Tehran threatened to target "all the facilities" of Kurdistan if militants were allowed to enter the Islamic republic.

So far, no forces have entered Iran, Iraq's border guards said.

The Iraqi government and the autonomous region said Friday that Iraq must not be a launchpad for attacks against neighbouring countries.