A highly sensitive and secure zone in Baghdad, where the US embassy is situated, was targeted with a series of rockets on Monday, according to reports. 

The attack on Monday is the third hostile attack in a week on western establishments in Iraq. 

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 had not fired because the rockets were not projected to land within the diplomatic compound, AFP reported.

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The headquarters of the Iraqi National Security Service, which is close to the US embassy, was hit by one of the projectiles causing serious damage in the area, according to AFP. 

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 a 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.

Washington said Monday it would hold Iran to account after the latest attack, but insisted it would not be drawn into an escalation.

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State Department spokesman Ned Price said the United States was "outraged" by recent attacks in Iraq, adding it would "hold Iran responsible for the actions of its proxies that attack Americans".

"What we will not do is lash out and risk an escalation that plays into the hands of Iran and contributes to their attempts to further destabilize Iraq," Price told reporters.

Mustafa Al-Kadhemi, the PM of Iraq, failed to place accountability on the groups responsible for the attack even after vowing to curb any such rocket attacks. 

With continued attacks in the region, the US in October threatened to withdraw its diplomatic mission to Iraq if the attacks did not teriminate.