The attack on Sunday evening in Baghdad’s fortified Green Zone marked a dangerous escalation in a series of rocket attacks in recent months that have targeted the embassy or Iraqi military bases where American troops are deployed.
None of the attacks has been claimed but Washington has repeatedly blamed Iran-backed military factions in Iraq.
On Sunday one rocket hit an embassy cafeteria at dinner time while two others landed nearby, a security source told AFP.
A senior Iraqi official told AFP at least one person was wounded, but it was not immediately clear how serious the injuries were and whether the person was an American national or an Iraqi staff member. Reuters reported three people had been wounded.
The US embassy did not immediately respond to requests for comment.
The US State Department called on Iraq late on Sunday to “fulfil its obligations to protect our diplomatic facilities”.
The Iraqi prime minister, Adel Abdel Mahdi, and the speaker of parliament, Mohammed Halbusi, both condemned the incident, saying it risked dragging their homeland into war.
Iraq has already been drawn into a worrying tit-for-tat between the US and Iran over the past month. A similar attack on a northern Iraqi base killed an American contractor, and the US retaliated with a strike on an Iran-backed faction known as Kataeb Hezbollah.
About 5,200 Americans are stationed in Iraq to lead the global coalition fighting IS, but the US strike on Baghdad has rallied top Iraqi figures around a joint call to order them out.
Vehemently anti-American cleric Moqtada al-Sadr organised a mass rally in Baghdad on Friday, where thousands of his supporters called for American troops to leave.
Sadr had previously backed separate anti-regime protests sweeping Iraq’s capital and south, even though he controls the largest bloc in parliament and top ministerial posts.
Bolstered by his own protest on Friday, Sadr announced he was dropping support for the youth-dominated reform campaign rocking the country since October.
His followers, widely regarded as the best-organised and well-stocked of the anti-government demonstrators, immediately began dismantling their tents and heading home.
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