The blasts near the Iranian, Egyptian and German embassies followed mortar attacks on the Iraqi capital's Green Zone, home to government buildings, official residences and foreign embassies. They came two days after gunmen slaughtered 24 people in a Sunni village south of Baghdad.
Iraqi authorities had warned of a possible escalation of violence because of rising tension after a March 7 parliamentary election that produced no clear winner.
"The terrorists seized this time between the end of the elections and the forming of the government to target the political process," said Abdul-Rasoul al-Zaidi, a civil defence official.
The bombers appear to have targeted embassies in the wealthy Mansour district. One bomb blew up in front of the main gate of the Iranian embassy, just outside the Green Zone. It destroyed about 30 cars and caused major damage to a nearby bank.
"This is enough. We are tired of explosions, we do not feel safe," said Jassim Mohammed, 39, who was driving a mini-bus with four passengers when the bomb exploded.
"We go out of our homes and we do not know whether we will come back or not," said Mohammed, who was wounded in the head, arm and leg.
Haider Karim, 32, said one of the blasts took place as a convoy was leaving the Egyptian embassy. The explosion left a large crater in the street in front of the embassy.
"Many security guards at the embassy were killed and wounded. I saw body parts at the scene," he said.
An Interior Ministry source said the three bombings killed at least 30 people and wounded 168. Baghdad security spokesman Major General Qassim al-Moussawi put the toll at 17 dead and 140 wounded.
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The car bombings followed a series of other incidents in the Iraqi capital. Two mortar rounds landed in the Green Zone early on Sunday and four on Saturday night.
A roadside bomb that targeted a police patrol in the capital on Sunday wounded five officers and five civilians. A bomb attached to a civilian vehicle in Baghdad's southern Saidiya district killed two people on Saturday.
The Iranian embassy had been a target before. In December 2009, a car bomb exploded in a car park near the mission, and seven months earlier gunmen fired on a car carrying three Iranian embassy staff.
Security forces had predicted a rise in violence after a tight election race that exposed the depth of Iraq's sectarian divide.
No political coalition won a majority of seats in parliament, and talks to form a government could take weeks or months.
A cross-sectarian coalition led by former Prime Minister Iyad Allawi won two seats more than a bloc led by Shi'ite Prime Minister Nuri al-Maliki.
Allawi's Iraqiya bloc won with strong support in Sunni-dominated provinces in the north and west, while Maliki won in predominantly Shi'ite provinces in the south.
On Friday gunmen invaded the Sunni village of Albusaifi south of Baghdad and killed 24 people, many of them execution-style with a gunshot to the head.
Authorities said many of the victims were members of the Sons of Iraq, former insurgents who joined U.S. forces to fight al Qaeda militants, helping to turn the tide of the war.