The attack is the third in a week to target Western diplomatic, military or commercial installations across Iraq after months of relative calm.

At least two rockets landed within the perimeter of the Green Zone, where the American and other foreign embassies are based, according to a statement by Iraq's security services.

A security source within the Green Zone said the C-RAM anti-rocket defence system deployed at the US embassy did not fire because the rockets were not projected to land within the diplomatic compound.

A security source told AFP at least one rocket hit the headquarters of Iraq's National Security Service near the US diplomatic mission, damaging several cars parked there.

A US-led coalition deployed in Iraq since 2014 to help local forces fight jihadists also operates a base near the American embassy.

"The coalition reports no damages or injuries," coalition spokesman Wayne Marotto said on Twitter.

At least one other rocket crashed into the nearby residential district of Harithiya, the military said.

A resident of the area told AFP the rocket damaged a multi-storey parking complex just a few metres from his home.

There was no immediate claim of responsibility for the attack, but the military said it had located the launchpad in a northern district of Baghdad.

The attack comes one week after more than a dozen rockets targeted a military complex at the Arbil airport in northern Iraq where US-led coalition troops are based.

Two people were killed, including one foreign contractor based at the airport, who died immediately, and a civilian, who succumbed to his wounds on Monday.

On Saturday, another wave of rockets hit the Al-Balad airbase north of Baghdad, where Iraq keeps most of the F-16s it has purchased from the US in recent years.

Security sources said at least one local contractor for Sallyport, the US company that maintains the planes, was wounded.

The attacks are usually claimed by shadowy groups that both Iraqi and US officials say are "smokescreens" for hardline pro-Iran factions inside Iraq.

Iraq's Prime Minister Mustafa al-Kadhemi has pledged to put a halt to rocket attacks but struggled to hold the groups to account, infuriating the US.

In October, the US threatened to close its embassy in Baghdad if the attacks did not stop, so hardline groups agreed to an indefinite truce.

There have been several intermittent violations since, but the past week has seen the most attacks in months.