The shock wave from the first blast near the international airport on Tuesday shook nearby buildings and was heard across the southwestern part of the capital.
Police said two civilians were killed in the blast.
Another car bomb exploded in the path of a US military convoy in al-Dura area south of Baghdad, Aljazeera reported.
A US Humvee and a civilian car were destroyed in the explosion.
A US soldier was killed in the incident, the army said.
One civilian was injured and brought to Yarmuk hospital in western Baghdad, a medical source said. Another person was reported to have been killed, but no further details were provided.
US forces cordoned off the area, while Iraqi forces prevented anyone from approaching it.
In other incidents, an Iraqi soldier and two US soldiers were killed on Monday in an intense battle with fighters northeast of Baghdad, the US military said on Tuesday.
Attacks on US forces have fallen
to 50 a day in recent weeks
"Coalition forces and Iraqi army soldiers encountered and attacked terrorist forces in a remotely populated region east of Baghdad at about 4pm (1200 GMT) on 4 April," a US military statement said.
A US marine was killed in action on Monday in Iraq's Anbar province west of Baghdad, the US military also said.
The marine was killed by "an explosion which occurred during combat operations".
In related news, police sources said a general in the Iraqi army had been abducted.
An Interior Ministry source said Brigadier-General Jalal Muhammad Salih and his bodyguards were pulled from his car by an armed group in the Mansur district of the capital at 11.30am (0730 GMT).
He was the commander in charge of the ministry's 1600-strong armoured brigade.
Iraqi police have found the corpses of 10 Iraqi soldiers buried in the Jurf al-Sakhr area, south of Baghdad, Aljazeera reported.
Corpses of executed Iraqi soldiers
are routinely found in Iraq
In Hilla, armed men killed a member of the Babil provincial council, Salim Hilal, as he was heading to work, Babil provincial police spokesman Captain Muthana Khalid said.
He said two suspects in the attack were arrested.
In the central city of Baquba, armed men wounded a government translator and killed her father in a drive-by shooting, Brigadier-General Adil Mulan of the Diala provincial police department said.
The US army has issued a statement revealing details of a riot at one of the prisons it runs in southern Iraq.
Inmates at Camp Bucca - the largest US-run prison in Iraq - hurled rocks and set tents on fire earlier this month, and four guards and 12 prisoners were wounded before the riot was brought under control on 1 April.
It said prisoners in one compound protested about the transfer of detainees to another compound.
"During the disturbance, the detainees chanted, threw rocks and set several of their tents on fire"
US Army statement
"During the disturbance, the detainees chanted, threw rocks and set several of their tents on fire," an army statement said.
"The disturbance was brought under control with only minor injuries to four guards and 12 detainees."
Last month, prison guards foiled a jailbreak by finding two tunnels dug under the ground at Camp Bucca. One of the tunnels had cleared the perimeter fence of the prison.
In January, US guards shot and killed four inmates during a riot at the same camp.