The assault sent warning sirens blaring across the high-security diplomatic compound but it was unclear exactly what was hit and how many rockets made impact, the source told AFP.
Multiple strong explosions followed by aircraft circling were heard near the Green Zone, the high-security enclave where the US embassy is located.
Sunday’s attack, before dawn, was carried out with “small rockets” and caused no casualties, a coalition spokesman said in a statement on Twitter.
The Green Zone is home to several Western embassies and government offices including the parliament, the prime minister’s office, and the presidency.
In recent months, however, the fortified zone has been repeatedly targeted by Katyusha rockets.
The Sunday attacks came a few weeks after the Islamic Revolution Guards Corps (IRGC) fired volleys of ballistic missiles at Ain al-Assad, a large airbase in Iraq’s Anbar hosting about 1,500 US troops, and another outpost in Erbil, the capital of the semi-autonomous Iraqi Kurdistan.
The missile operation was in response to Washington’s January 3 assassination of top Iranian general Qassem Soleimani, who led the IRGC’s Quds Force.
The assassination also resulted in the death of Abu Mahdi al-Muhandis, who was the second-in-command of Iraq’s Popular Mobilization Units (PMU).
Iraqi resistance groups have vowed to avenge the assassination of Abu Mahdi, as Iran took revenge for General Soleimani.