Meanwhile, a least one anti-government protester was shot dead in Baghdad and another in the flashpoint southern city of Nasiriyah as security forces use live rounds and tear gas to try to flush protesters out of squares and streets.
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 of protesters kept up anti-government sit-ins across the country.
The nighttime rocket attack injured one personnel member and caused some material damage, staffers there said on Monday.
The two staff members, who spoke on condition of anonymity because they were not authorised to brief the media, did not specify the injured person's nationality or the severity of their wounds. They said the rocket slammed into a restaurant inside the embassy compound.
The US Embassy is within the Iraqi capital's Green Zone, and has been a flashpoint amid wider regional tensions between the U.S. and Iran, which have played out inside Iraq in recent weeks.
Iraqi supporters of an Iran-backed militia stormed the embassy compound on December 31, smashing the main door and setting fire to the reception area.
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.
The US embassy did not immediately respond to requests for comment.
The US State Department called on Iraq late Sunday to "fulfil its obligations to protect our diplomatic facilities".
The attack took place earlier in the day than usual, with AFP reporters hearing the booms on the western bank of the river Tigris at precisely 1630 GMT (7:30 pm local time).
Iraqi Prime Minister Adil Abdul Mahdi and Speaker of Parliament Mohammed Halbusi both condemned the incident, saying it risked dragging their homeland into war.
At least five katyusha rockets landed in the heavily fortified Green Zone in Iraq’s capital, some of which directly struck the US embassy, caretaker Prime Minister Abdul Mahdi said early on Monday.
"This hostile attack on a foreign mission was repeated with missiles falling inside the US embassy compound. While condemning this illegal act, we instructed our security forces to arrest the attackers and bring them to justice," Abdul Mahdi said in a statement
He added that this kind of attack could turn Iraq into a conflict zone.
No casualties or material damage has been reported so far.
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 outside the Baghdad airport – prompting Iran to fire ballistic missiles at an Iraqi air base where US troops are stationed.
Washington had earlier denied any of its personnel were injured in the Iranian strike but later on Friday the Pentagon disclosed that 34 US service members suffered traumatic brain injury
The Pentagon added that half of those injured have returned to work, but the casualty total belies President Donald Trump's initial claim that no Americans were harmed. He later characterised the injuries as “not very serious.”
Anti-government protests continue
Violence between Iraqi security forces and anti-government protesters also continued to seethe overnight, with one protester shot dead in a violent crackdown in the country's south. Unrest was also ongoing in the capital, with new clashes erupting Monday near the central Khilani Square, where security forces fired tear gas to disperse crowds.
Security forces also chased after demonstrators and beat them.
A female anti-government protester was overpowered, dragged by the hair and pinned down by a member of the security forces outside Baghdad's municipality building. The incident, captured by an Associated Press photographer, was a rare occurrence in the largely male-dominated front-lines of the demonstrations.
The security personnel conducted a search of the female protester and tore off a protective face mask she was wearing as a witness threw stones.
'Only for you, Iraq!'
Some 5,200 Americans are stationed in Iraq to lead the global coalition fighting the defeated Daesh terrorist group, but the US strike on Baghdad has rallied top Iraqi figures around a joint call to order them out.
Vehemently anti-American cleric Muqtada 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.
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.
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.
In the capital, riot police have tried to clear streets around the main protest camp of Tahrir Square but have yet to enter the symbolic area, where many protesters stood their ground even after tents there were dismantled.
Just after midnight in Nasiriyah, unknown assailants stormed the main protest camp in Habbubi Square and set the tents on fire, the flames lighting up the night sky, an AFP correspondent there said.
UN hails 'Iraqi hopes'
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.
In Basra, hundreds of students gathered to condemn the riot police's dismantling of their main protest camp the previous day, according to an AFP correspondent.
The youth-led protests erupted on October 1 in outrage over lack of jobs, poor services and rampant corruption before spiralling into calls for a government overhaul after they were met with violence.
More than 470 people have died, a vast majority of them demonstrators, since the rallies began.
Protesters are now demanding snap elections, the appointment of an independent premier and the prosecution of anyone implicated in corruption or recent bloodshed.