The US Embassy is seen from across the Tigris River in Baghdad, Iraq, on Jan 3, 2020. (PHOTO / AP)

Approximately seven mortar rounds landed in the US Embassy compound in Baghdad during an attack early on Friday, a US military official told Reuters, in what appeared to be the largest attack of its kind in recent memory.

US forces in Iraq and Syria were also targeted with rockets and drones at least five more times on Friday; three times at separate bases in Syria, and twice at the Ain al-Asad airbase west of Baghdad, a different US defense official said.

The attacks were the most recorded against US forces in the region in a single day since mid-October, when Iran-aligned militias started targeting US assets in Iraq and Syria over Washington's backing of Israel in its war against Hamas in Gaza.

US Defense Secretary Lloyd Austin, in a call with Iraq's Prime Minister Mohammed Shia Al-Sudani, condemned the attacks and singled out Iran-aligned armed groups Kataib Hezbollah and Harakat Hezbollah al Nujaba for the recent targetting of US personnel.

"The United States reserves the right to respond decisively against those groups," Austin told Sudani, according to a Pentagon statement summarizing the call.

The embassy attack marked the first time it had been fired on in more than a year, apparently widening the range of targets. Dozens of military bases housing US forces have been attacked, increasing fears of a broadening regional conflict.

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No group claimed responsibility, but previous attacks against US forces have been carried out by Iran-aligned militias operating under the banner of the Islamic Resistance in Iraq.

The US military official, speaking on the condition of anonymity, left open the possibility that more projectiles were fired at the embassy compound but did not land within it.

The US officials said Friday's attacks caused no injuries, and the embassy attack caused very minor damage.

Reuters was first to report the number of mortars that hit the embassy compound.

The US has responded with a series of strikes that have killed at least 15 militants in Iraq and up to seven in Syria

Explosions were heard near the embassy, in the center of Baghdad, at about 4 am (0100 GMT) on Friday. Sirens calling on people to take cover were activated.

State media said the attack damaged the headquarters of an Iraqi security agency.

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The US has responded with a series of strikes that have killed at least 15 militants in Iraq and up to seven in Syria.

The State Department called on the Iraqi security forces to immediately investigate and arrest the perpetrators.

'Acts of terrorism'

The attacks pose a challenge for Sudani, who has pledged to protect foreign missions and capitalize on fragile stability to focus on the economy and court foreign investment, including from the United States.

Sudani directed security agencies to pursue the perpetrators, describing them as "unruly, lawless groups that do not in any way represent the will of the Iraqi people," a statement from his office said.

He also said that undermining Iraq's stability, reputation and targeting places Iraq has committed to protect were acts of terrorism.

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Aside from its diplomatic staff in Iraq, the United States has about 2,500 troops in the country on a mission it says aims to advise and assist local forces trying to prevent a resurgence of Islamic State, which in 2014 seized large swathes of both Iraq and Syria before being defeated.