A second blast, about 30 minutes later, shook buildings in the centre of the city and sent thick clouds of black smoke pouring into the air above one of several hotels used by foreign contractors and workers.
In the first attack on Monday, witnesses said a car raced towards one of several entrances to the Green Zone, home to the Iraqi interim government, but detonated before reaching the gate, exploding near a recruitment post for the US-established Iraqi National Guard.
In the second explosion, on the other side of the Tigris river on one of Baghdad's main streets, a large bomb detonated as a convoy of US military vehicles was passing, witnesses said.
The explosion occurred in front of the Baghdad Hotel, a building used by US contractors and government personnel.
A doctor at nearby Yarmuk hospital said eight people were killed and 30 wounded in the first explosion, several of them civilians who were passing by when the bomb went off.
At least four people were killed and a dozen wounded in the second, Iraq's Interior Ministry said.
The Mosul attack killed seven
people including two children
The second blast destroyed several cars, shattered dozens of shop windows and sprayed wreckage across the street, leaving a car door hanging from a street sign.
The US military said no soldiers were killed or wounded.
In a third attack, a car bomb exploded outside a primary school in the northern city of Mosul, killing seven people, including two children, police said. Eleven people were wounded.
Six children were among those wounded, Aljazeera's correspondent reported.
The car, driven by two men, may have exploded prematurely, a US officer at the scene said, as there was no obvious target in the area, a quiet district in the south of the city.
In a separate development, two US soldiers were killed in an attack with small arms at a traffic control checkpoint in the Iraqi capital on Sunday, the US military said on Monday.
Indonesian women released
Also on Monday, two Indonesian women taken captive in
Iraq were released and were handed over to the United Arab Emirates embassy in Baghdad, Abu Dhabi TV reported.
The two captives were identified as Rosidah binti Anom and Rafikan binti Amin.
Foreign ministry spokesman Marty Natalegawa said Indonesia's embassy in Abu Dhabi was trying to make contact with the United Arab Emirates embassy.
Earlier, al-Jaish al-Islami in al-Iraq, (Islamic Army in Iraq) the group which claimed to have captured the two women, said it would release them if Jakarta freed Muslim cleric Abu Bakr Bashir, who is being held for alleged terrorist links.
Children and women are again
victims of Falluja air raids
Overnight, the US military continued its offensive on Falluja, carrying out another wave of air strikes.
A strike in the central Jumhuriya area killed nine people, including three women and four children, said Dr Adil Khamis of Falluja general hospital.
Twelve were injured, including six women and three children, he said. They included residents of neighbouring houses that were damaged in the attack.
Iraqi journalist Abu Bakr al-Dulaimi told Aljazeera that nine people had been killed. He said the two targeted homes were completely destroyed and two nearby houses damaged.
The reporter described Falluja as almost paralysed, with shops and schools closed.
At dawn American warplanes unleashed strikes on two houses in Falluja, killing at least 11 people, including women and children.
The US military again said the strikes targeted followers of al-Qaida-linked Abu Musab al-Zarqawi and their associates.
The strike in the city's southern al-Shuhada neighbourhood killed two people.
It was the latest in weeks of air strikes on the city west of Baghdad which has left scores of Iraqi civilians dead.