Rockets were fired towards the heavily fortified Green Zone in Iraq's capital Baghdad early on Friday morning, senior Iraqi security officials told The National.
The area houses the US embassy, other diplomatic missions and Iraqi government offices.
Explosions were heard near the US embassy at about 4am on Friday.
The US embassy was attacked by “two salvos of rockets”, a representative said.
“Assessments are ongoing but there are no reported casualties on the embassy compound,” the embassy said.
“At this point, no specific group has claimed responsibility but indications are the attacks were initiated by Iran-aligned militias, which operate freely in Iraq.”
An alert called for people to “duck and cover”, social media videos showed.
“We again call on the government of Iraq, as we have done on many occasions, to do all in its power to protect diplomatic and coalition partner personnel and facilities. We reiterate that we reserve the right to self-defence and to protect our personnel anywhere in the world,” the US embassy said.
Iraqi Prime Minister Mohammed Shia Al Sudani for the first time described such attacks as “acts of terrorism” and ordered an investigation and the arrest of those responsible.
“Targeting diplomatic missions is unjustifiable and unacceptable under any circumstances, regardless of the claims and illusions behind these reprehensible actions,” he said.
“The perpetrators of these attacks harm Iraq, its stability and security.
“The outlawed groups do not represent the will of the Iraqi people and do not reflect the national decision expressed by the Iraqi government in the official occasions.”
The UN Assistance Mission for Iraq also condemned the attack, saying diplomatic premises must be protected in line with international law.
“We reiterate that Iraq's stability and security are front and centre in all our engagements,” it said on X, formerly Twitter. “Iraq cannot afford to be drawn into a wider conflict, which would threaten hard-won stability and the achievements made so far.”
US troops stationed at military bases in Iraq and Syria have faced more than 70 attacks since mid-October.
The attacks have been mostly claimed by an umbrella organisation of Iraqi Shiite groups, although diplomatic missions have so far been spared.
No group immediately claimed responsibility for the Green Zone attack.
Reuters contributed to this report