"We have made the point before that the actions of lawless Iran-backed militias remains the single biggest deterrent to stability in Iraq," State Department spokeswoman Morgan Ortagus said in a statement.

Monday's attack -- one of around 40 targeting US interests since early August -- comes after Washington threatened to close its embassy and withdraw its remaining 3,000 troops if the violence does not end.

"These militias pose an unacceptable danger to everyone in Iraq, from diplomatic officials and facilities to Iraqi activists and families," Ortagus said.

Five children and two women were killed by the rocket that was targeting the nearby Baghdad airport Monday.

Iraq has long been caught in a tug-of-war between its allies Iran and the US, rendered rockier by Washington's "maximum pressure" policy against Tehran since 2018.

Possibly anticipating a backlash, pro-Iran social media accounts that usually laud such rocket strikes were silent in the wake of Monday's attack.

"We express our condolences to the innocent Iraqi people and their families who were victims, once again, of these ruthless acts of violence," Ortagus said.

"The Iraqi people deserve to live in safety and security, so we call on Iraqi officials to take immediate action to hold the perpetrators accountable," she added.

In addition to around 3,000 troops stationed in three bases across the country, the US still has hundreds of diplomats in its mission in Baghdad at the high-security Green Zone.