Salvoes of rockets were launched early Friday at the US embassy in Baghdad's heavily fortified Green Zone, the mission said, the latest in a flurry of such attacks amid the Israel-Hamas war.
"A multi-rocket attack was launched at US and Coalition forces in the vicinity of Union III and the Baghdad embassy complex" without causing any reported casualties or damage, a US official said.
There was no immediate claim of responsibility.
The United States leads an international coalition battling jihadists in Iraq and neighbouring Syria, and its forces have come under repeated attack in recent weeks.
On Friday, there were a further five attempted strikes against US and coalition troops.
Drone or rocket attacks were launched twice against the Ain al-Asad airbase in western Iraq and three bases in Syria were targeted, according to a US military official speaking anonymously, reporting "no casualties and no damage".
The attacks come against a backdrop of the more than two-month war between US ally Israel and the Iran-backed Palestinian militant group Hamas in Gaza.
The United States "strongly" condemned the attacks and called on Iraq to bring the perpetrators to justice, the State Department said in a statement.
"The many Iran-aligned militias that operate freely in Iraq threaten the security and stability of Iraq, our personnel, and our partners in the region," spokesman Matthew Miller said in the statement.
The US embassy said "two salvoes of rockets" were fired at the mission compound in Baghdad at around 4:15 am (0115 GMT).
"Indications are the attacks were initiated by Iran-aligned militias," said a US spokesperson.
"The Iraqi government has repeatedly committed to protect diplomatic missions as well as US military personnel, who are present in the country at Iraq's invitation," Miller said.
"This is non-negotiable, as is our right to self-defense."
- Balancing act -
Iraqi Prime Minister Mohammed Shia al-Sudani warned that attacks on embassies undermine the country's security and called on security forces to bring those responsible to justice.
Brought to power by a pro-Tehran coalition, Sudani faces a difficult balancing act between the United States and Iran.
Since mid-October there have been dozens of rocket or drone strikes by pro-Iran groups against US or coalition forces in Iraq, as well as in Syria.
But Friday's rocket attack was the first against the US embassy in Baghdad since the Israel-Hamas war began on October 7, raising regional tensions and fears of a wider conflict.
An Iraqi security official said "three Katyusha rockets targeting the American embassy fell close to the Green Zone", near the river Tigris.
There are roughly 2,500 US troops in Iraq and about 900 in Syria as part of efforts to prevent a resurgence of the Islamic State group.
Pro-Iran groups have justified their attacks by pointing to American support for Israel.
In Iraq, most were claimed by the Islamic Resistance in Iraq, a loose formation of armed groups affiliated with the Hashed al-Shaabi coalition of former paramilitaries that are now integrated into Iraq's regular armed forces.
US forces have struck Iran-linked targets in Iraq and Syria in response.
Late on Friday, the Coordination Framework -- an alliance of powerful pro-Iran Shiite factions, and the largest grouping in Iraq's parliament -- denounced the embassy attack.
It said it wanted to "preserve the security of diplomatic missions" and rejected "any terrorist attack targeting the security and sovereignty of the country".
Sudani said Friday's attacks were "unacceptable and unjustifiable".
"Our security forces... will continue to protect embassies," the Iraqi premier said.
His foreign affairs adviser, Farhad Alaaldin, said the government was "determined" to uphold Iraq's stability.
- More than 80 attacks -
The UN Assistance Mission for Iraq also condemned the attack and warned of repercussions.
"Iraq cannot afford to be drawn into a wider conflict," UNAMI said on X, formerly Twitter.
Separately, on Friday evening an explosive drone struck a civilian building in Arbil, the capital of northern Iraq's autonomous Kurdistan region, without causing any casualties, the Kurdish counter-terrorism service said without giving further details.
Washington has counted at least 84 attacks since October 17 against its forces in Iraq and Syria.
The attacks against US personnel have left at least 60 US personnel wounded, the Pentagon says.
The Israel-Hamas war began when Hamas gunmen attacked Israel on October 7, killing about 1,200 people, mostly civilians, and taking around 240 hostages, Israeli officials say.
In response, Israel vowed to destroy Hamas and launched a massive military offensive that has killed 17,487 people in Gaza, according to the territory's health ministry.