The violence came as Washington announced a historic cut in its troop numbers in Iraq and Afghanistan.

According to the Iraqi military, four of the rockets landed in the high-security Green Zone, where the US embassy and other foreign missions are based.

Another three rockets also hit other parts of Baghdad, killing one girl and wounding five civilians.

All seven rockets were launched from the same location in east Baghdad, the Iraqi military said in a statement.

AFP reporters heard several large blasts, followed by rapid-fire sounds and red flares lighting up the sky, indicating that the embassy's C-RAM rocket defence system was deployed.

A spokesman for the US-led coalition said Iraqi intelligence had confirmed a rocket attack on the US embassy but declined to comment on the C-RAM usage.

Since October 2019, nearly 90 deadly rocket attacks and roadside bombs have targeted foreign embassies, troops and other installations across Iraq.

The attacks have been claimed by groups described by both US and Iraqi officials as "smokescreens" for hardline Iran-aligned factions in Iraq.

The US has explicitly named Kataeb Hezbollah as behind some of the violence and has twice bombed the group.

The attacks infuriated Washington, which has pressured Iraqi Prime Minister Mustafa al-Kadhemi to take tougher action against the perpetrators.

Last month, the US issued an ultimatum to Kadhemi's government, threatening to close down its diplomatic compound in Baghdad if the rockets did not stop.

- Troops to trickle out -

The escalation prompted pro-Iran factions to announce a truce for an unspecified amount of time. The rockets immediately halted, with Tuesday's attack the first in more than a month.

It came just hours after US Secretary of State Mike Pompeo, who Iraqi sources said had relayed the threat to close the embassy, called Kadhemi.

Around the same time, the US announced it would slash troop levels in Afghanistan and Iraq to 2,500 in each country, their lowest levels in nearly 20 years of war.

Washington still has some 3,000 troops stationed across Iraq as part of the US-led coalition helping the country fight the Islamic State group since 2014.

The coalition had already significantly drawn down its troop levels this year, partly due to Covid-19 travel restrictions

But the troop presence irks Iraq's eastern neighbour and key ally Iran, which has insisted the US should militarily withdraw from the entire Middle East.

Tehran has ramped up those calls since January, when a US drone strike in Baghdad killed top Iranian general Qasem Soleimani and a leading Iraqi paramilitary official.

Outraged by the strike, Iraq's parliament voted for all foreign troops to leave the country and pro-Tehran factions have organised a series of demonstrations against the US military.

The Kadhemi-led government has slow-walked the decision, and instead launched a strategic dialogue with the US on military, diplomatic and economic issues.

Iraqi officials told AFP they hope the dialogue will continue as planned after President-elect Joe Biden takes over the US administration in January.

But they see a turbulent few months ahead: the officials expect President Donald Trump to unleash a "bucket-list of sanctions" on Iranian entities, including some operating in Iraq.

They did not rule out last-minute military action by the Trump administration on Iranian interests in Iraq.

And they confirmed the US had continued with its planning for an embassy withdrawal despite last month's truce.