In the first attack on Tuesday, a car bomber blew up his vehicle near a US military convoy in central Baghdad, killing at least eight Iraqis and wounding 16, Iraqi journalist Walid Khalid reported.
The injured were transferred to three hospitals; Ibn al-Nafis, Baghdad and al-Kindi in central Baghdad, Khalid added.
Khalid told Aljazeera that witnesses said the real number of casualties was much higher than that announced, due to the huge crowds present at the explosion scene.
More than 15 civilian cars and dozens of shops were damaged in the explosion, he added.
Tuesday's explosion occurred in al-Nasr Square, a main intersection of shops, offices and apartment buildings near the Tigris river, witnesses and a TV report said.
The first blast at 9.40am rattled windows in the city centre and thick black smoke rose into the sky.
The second car bomb exploded at about 11am (0700 GMT) on Abu Nawas street, in the southern Jadriya neighbourhood.
Eight Iraqis were killed in the car
bomb attack on Tuesday
Khalid said the explosion targeted the headquarters of al-Nahriya (river) police in Abu Nawas street, severely injuring three policemen.
A huge fire erupted in the police building, badly damaging it along with houses close by.
Also on Tuesday, US forces continued their attack on the northern banks of the Euphrates river in their hunt for fighters, in an area near the Syrian border the US says serves as a staging post for Iraq's most wanted man, Abu Musab al-Zarqawi.
Operation Matador, the largest US combat engagement this year, involved a unit of about 1000 men attacking areas of al-Anbar province, in the northwest of the country, a US military spokesman said.
US forces said on Monday they had killed 75 Iraqi and foreign rebels, but al-Zarqawi's group immediately denied that 75 had been killed and also denied any of its leaders had been arrested, in internet statements posted on Monday.
There was no update on the toll on Tuesday and no indication of any US casualties in Monday's operation.
Reward for al-Janabi
The Iraqi government also announced on Tuesday it was offering $50,000 for information leading to the capture of a Sunni Muslim leader who is said to have led Falluja for six months last year.
"The Iraqi government announced a $50,000 reward for information leading to the arrest of Abdullah al-Janabi," it said in a statement.
"Janabi is wanted for providing financial, and manpower support to terrorist groups who come from outside the country," it added.