“This apparent act of terrorism, which we strongly condemn, was directed at the heart of the Iraqi state,” State Department spokesman Ned Price said in a statement.
“We are in close touch with the Iraqi security forces charged with upholding Iraq’s sovereignty and independence and have offered our assistance as they investigate this attack.”
A large number of security forces were deployed in and around the heavily-guarded Green Zone, which also hosts the US embassy and is frequently targeted by rocket attacks.
On 31 October, three rockets fell in Mansour, a neighbouring district, without causing any injuries.
The attack came during a period of soaring tensions over the results of the 10 October elections.
Preliminary results saw the Conquest (Fatah) Alliance, the political arm of the pro-Iran multi-party Hashed al-Shaabi paramilitary network, suffer a substantial decline in its parliamentary seats.
The group’s supporters have denounced the outcome as “fraud”.
Hundreds of Hashed supporters clashed with police on Friday while protesting near the Green Zone to vent their fury over the result.
One protestor died of their injuries in hospital, according to a security source, while a Hashed source said two demonstrators were killed.
The health ministry reported 125 injuries, most of them from the security forces.
Several hundred supporters of pro-Iranian groups returned to the Green Zone on Saturday to protest.
Some burned a portrait of the prime minister, whom they called a “criminal”.
According to preliminary tallies, the Conquest won around 15 of the 329 seats in parliament last month, down from the 48 it held previously, which made it the second-largest bloc.
The big winner this time, with more than 70 seats according to the initial count, was the movement of Moqtada Sadr, a Shiite Muslim preacher who campaigned as a nationalist and critic of Iran.
Final election results are expected within weeks.