"Yesterday, Katyusha rockets were fired at the US embassy, and this is painful and incorrect ... Who authorises those parties to attack the embassy in Iraq?," Xinhua news agency quoted Mahdi's office as stating after the weekly cabinet meeting on Tuesday.
"This act offends Iraq and is unacceptable regardless of their intentions," Abdul Mahdi said without naming the attackers.
Late on Monday, an Iraqi Interior Ministry's official told Xinhua that three Katyusha rockets landed near the US embassy in the heavily fortified Green Zone in central Baghdad without causing casualties.
The heavily fortified Green Zone has been frequently targeted by insurgents' mortar and rocket attacks. The roughly 10-square-km zone is located on the west bank of the Tigris River, which bisects the Iraqi capital.
No group has so far claimed responsibility for the attack which came after growing tensions between the US and Iran.
On January 8, Iran fired ballistic missiles on military bases housing US troops in Iraq's western province of Anbar and near the city of Erbil, the capital of the semi-autonomous region of Kurdistan.
The Iranian attack came after a US drone attacked on January 3 a convoy at Baghdad International Airport, killing Qassem Soleimani, commander of the Quds Force of Iran's Islamic Revolution Guards Corps, and Abu Mahdi al-Muhandis, deputy chief of Iraq's paramilitary Hashd Shaabi forces.
More than 5,000 US troops have been deployed in Iraq to support the Iraqi forces in the battles against Islamic State militants.
( With inputs from IANS )