The first round of explosions occurred about at 10pm (18:00 GMT) on Monday and another round struck at about 10am on Tuesday.
Lieutenant-Colonel Christopher Garver, the US military spokesman, said no military personnel were injured and no equipment was reported damaged in Monday's strike.
An Iraqi government official said six mortar rounds fell around the offices of Nuri al-Maliki's office and the closest came within 100m of the compound.
Deadly attacks
Meanwhile, Al Jazeera reported that at least 21 Iraqis died in separate attacks in Baghdad, while the number of US soldiers killed in April exceeded 100.
At least 11 civilians were killed and three others, including a man and a child, were wounded when armed men attacked a bus on the main road in the Iskandariya neighbourhood of south Baghdad, an Iraqi security source said.
A group of fighters standing on the highway opened fire at civilian cars, killing three people and wounding five near Latifiya, a town 40km south of the capital and about 10km north of the site of the Iskandariya attack.
Another four people were killed when a salvo of mortar rounds rained down on Latifiya.
A number of Kurdish peshmerga fighters serving in the Iraqi army and some Mahdi Army militia members were killed during a two-hour gun battle in Baghdad's Bayaa district, Iraqi police sources said.
Bodies found
Iraqi police have found 27 dead bodies during the past 24 hours in various neighbourhoods in Baghdad, Iraqi police sources said.
At least 10 people were killed and 15 others injured in mortar shelling of north Baghdad's Husainiya district, medical sources at Sadr City's Imam Ali Hospital said.
Overall, the death toll among Iraqis was down in April, according to government figures, with 1,689 deaths, nearly 20 per cent less than in March, due to the drop in sectarian killings.
US toll rises
Five US soldiers were killed in al-Anbar province and Baghdad over the weekend.
This pushed the number of US soldiers killed in April to 104, a US state department report said.
Separately, the Hamas al-Iraq group has released footage saying it has destroyed a US military vehicle in Muqdadiya city, east of Baghdad.
The video shows a roadside bomb explosion striking a military vehicle. However, Al Jazeera could not verify the authenticity of the tape.