Twenty-five others were wounded in the first explosion outside the city hall building and near a school in Mosul, 360km northwest of Baghdad.
Hospital sources told Aljazeera that three people had been killed and at least 38 others injured in the blast.
Body parts were hurled on the streets and nine vehicles were set on fire. The building was not damaged.
Witnesses saw three bombers in an orange and white taxi, the US military said.
Doctors said some of the dead were charred beyond recognition after the deafening explosion. Pictures from the scene showed a massive tangle of charred wreckage in the street.
The US military said the target of the attack was a convoy carrying members of the provincial council and Mosul's deputy police chief. City hall officials said the mayor, who heads the provincial security commission, was also targeted.
The provincial officials and mayor were not harmed in the blast, while the deputy police chief received minor injuries. The mayor's office said several of his bodyguards were injured.
The second blast took place about 45 minutes later outside an occupation operating base. There was no word on casualties.
In the earlier attack on Tuesday, a car blast outside a US base in Baquba killed at five people and wounded several others.
US occupation soldiers cleared the area at the former Iraqi air force base, north of the capital, now used by the US Army's 1st Infantry Division.
The US military confirmed an explosion, but could provide no further details.
The explosion occurred in Baquba at rush hour, 10 metres from the main gate to the airport al-Faris, said Iraqi police Second Lieutenant Ali Hussain. He said there were 12 injured and four dead among the Iraqis.
Up to 20 people were wounded
in the Baquba blast
Aljazeera's correspondent reported at least five people had been killed.
"The car bomb happened at 8am by the base entrance where many Iraqis gather to enter for work," said witness Ziad Mahmud, who is employed on the base, 60km northeast of Baghdad.
A red Mitsubishi sped into the cement barriers outside the US base, used by the 1st Infantry Division, and burst into flames, Mahmud said.
Witnesses told Aljazeera the driver of the vehicle jumped out moments before the explosion.
Others said the explosion caused a number of US casualties from those who search Iraqi workers at the entrance.
However, the US military refused to comment on the reports, the correspondent added.
The blasts are the latest in a series of attacks on US occupation forces and their allies in the days leading to the handover of power in Iraq on 30 June.
A car bomb exploded on Sunday near the gate of another US-run base north of Baghdad, killing six people and injuring 20 others - including two American soldiers, the US military said.
Meanwhile, five occupation soldiers were killed clearing mines in the Polish-run zone in Iraq, a Polish military spokesman said on Tuesday.
"During a demining operation an accidental explosion killed five coalition soldiers: two Poles, two Slovaks and one Latvian," said Colonel Zdzislaw Gnatowski, spokesman for Poland's general staff.
Gnatowski said several other soldiers were injured.