Three rockets score direct hits on the US embassy in Baghdad in latest round of missiles aimed at heavily fortified Green Zone

Three rockets slammed into the US embassy in Iraq's capital on Sunday in the first direct hit reported after months of close calls, as thousands kept up anti-government sit-ins across the country.

The attack marked a dangerous escalation in the spree 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 said.

The US embassy building  in the heavily fortified Green Zone in central Baghdad, Iraq

The US embassy did not immediately respond to requests for comment, but a statement by Iraqi security forces earlier in the evening told AFP there were no casualties.

The attack took place earlier in the day than usual, with bombs being heard on the western bank of the river Tigris at precisely 7:30 pm (1630 GMT).

Iraqi Prime Minister Adel Abdel Mahdi and Speaker of Parliament Mohammed Halbusi both condemned the incident, saying it risked dragging their homeland into war.

Iraq has already been dragged into a worrying tit-for-tat between the United States and Iran over the last 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.

Less than a week later, a US drone strike killed Iranian general Qasem Soleimani and Iraqi military figure Abu Mahdi al-Muhandis outside the Baghdad airport - prompting Iran to fire ballistic missiles at an Iraqi base where US troops are stationed.  

Iraqi demonstrators wave the national flag during an anti-government rally in the southern city of Basra on Sunday

Some 5,200 Americans are stationed in Iraq to lead the global coalition fighting the Islamic State group, but the US strike on Baghdad has rallied top Iraqi figures around a joint call to order them out.

Vehemently anti-American cleric Moqtada 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.

Anti-government protesters gather at Tahrir square in Iraqi capital Baghdad on Sunday

Activists feared that without his political cover, authorities would move to crush their movement - and indeed, within hours, riot police tried to storm protest camps across the capital and south.

Those efforts continued into Sunday, with security forces using live rounds and tear gas to try to flush protesters out of squares and streets they had occupied for months.

One protester was shot dead in Baghdad and another in the flashpoint southern city of Nasiriyah, medical sources said, and dozens more were wounded across the country.

Despite the renewed violence, thousands of students flooded the streets in the capital and across the south in a bid to keep national attention focused on their demands.

'Only for you, Iraq!' read a sign held by a young protester in the shrine city of Karbala, hinting at the movement's insistence on not being affiliated with any political party or outside backer.