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Rockets struck a military base located near the US embassy in Baghdad's heavily fortified Green Zone early on Sunday morning, as Iran-backed Shia paramilitary groups continue to vow revenge for the killing of a senior Iranian commander in a US drone strike last month.

An official spokesman for the US-led coalition in Iraq, Col. Myles Caggins, confirmed on Twitter that a 'small rocket' impacted the base housing US troops and other coalition forces just before 3.30 A.M local time.

The attack caused no casualties and only minor damage was reported, added Caggins.

A senior US military official, however, said the base was rocked by multiple explosions after 'a series of strikes', according to Reuters. 

Read more: Rockets strike Iraq base hosting US troops: military

Citing other US and Iraqi officials, AP report that at least four rockets had landed near the sprawling US embassy.

Three Iraqi officials who spoke on a condition of anonymity, claimed two rockets fell directly inside the US embassy compound, while another hit nearby the coalition base.  

There was no immediate claim of responsibility for the attack, which struck Baghdad's Green Zone, the high-security enclave that is home to countless foreign embassies and government offices. 

On Friday, a mortar shell exploded in the K1 military airbase in Kirkuk province in northern Iraq, the same base where Iran-backed militia killed a US military contractor in strikes in December last year.

Sunday's attacks came shortly after a leader in Iraq's Al-Nujaba movement, a faction of al-Hashed al-Shaabi, the Iran-backed paramilitary network officially incorporated into the state, had announced the begining of a 'countdown' for strikes on US forces in the country. 

The faction's leader Akram al-Kaabi tweeted a photograph of what he claimed was an American military vehicle, adding: "We are closer than you think."

Attacks on US military forces and assets in the country have increased in frequency and intensity since US President Donald Trump ordered drone strikes that killed the leader of Iran's elite Quds force, Qasem Soleimani, along with deputy commander of the Iraqi paramilitary, Abu Mahdi Al-Muhandis.

The US embassy in Baghdad has been a flashpoint amid wider US-Iran tensions in the region, which have played out inside Iraq in recent weeks.

Iraqi supporters of an Iran-backed militia stormed the embassy compound Dec. 31, smashing the main door and setting fire to the reception area.

Last month, the Iraqi parliament passed a resolution calling for an end to the presence of foreign troops linked to the US-led alliance fighting the Islamic State militant group in the country.

There are currently approximately 5,000 US troops stationed in Iraq.

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