The explosions occurred at midmorning in a religiously mixed neighborhood controlled by a major Shiite party, two days after President Bush approved plans to send more U.S. and Iraqi troops into the capital city to curb rising sectarian violence.
Several mortars landed in the district, some destroying a bank and an apartment building that later collapsed in flames, said Interior Ministry secretary Saadoun Abu al-Ula. The others exploded in the middle of busy streets crowded with traffic.
The car bomb exploded near a gas station, shattering storefronts and spraying flaming gasoline onto homes and stores, the Interior Ministry said. Charred hulks of trucks overturned on the streets. The front of an apartment complex was shorn away by the blast.
The explosion occurred about 200 yards way from the house of Vice President Adil Abdul-Mahdi, a Shiite and a senior figure in the Supreme Council of the Islamic Revolution in Iraq.
The mortars all landed in mainly commercial areas, with one exploding about 150 yards from SCIRI's headquarters in Karradah.
The attack was the largest on Karradah, a mixed neighborhood but mostly Shiite, in about a year. The area includes the home of President Jalal Talabani and the head of SCIRI, Abdul-Aziz al-Hakim.
Police Col. Abbas Mohammed Salman put the casualty toll as 31 dead and 153 wounded but said the deaths could rise because many of the injuries were severe.
In other developments:
Dozens of dazed, blood-soaked survivors shuffled through the rubble as emergency crews loaded weeping victims into ambulances, witnesses said.
The complex attack occurred as Iraqi Prime Minister Nouri al-Maliki was en route home from Washington, where he discussed the deteriorating security situation with President Bush. The president agreed to send more U.S. soldiers onto Baghdad streets to try to curb sectarian violence.
A steady rise in violence since al-Maliki's government took office May 20 has drawn new attention to sectarian militias and death squads, whose tit-for-tat killings have raised fears the country has begun to unravel.
Britain's ambassador to Iraq said Thursday that the security problem was made all the worse because Iraqis have lost confidence in the police.
Speaking on BBC Radio 4's "Today" program, William Patey said evidence suggests some members of the police are linked to Shiite militias and Sunni insurgent groups.
"Undoubtedly the Iraqi people have lost confidence in the police," Patey said. "You move from optimism and pessimism. It's a fine dividing line."
Also Thursday, gunmen killed four security guards outside a Sunni mosque in western Baghdad, police said.
During his to a joint session of Congress, al-Maliki insisted that his country is a front line in the war on terrorism and said those behind rampant violence are perverting the Islamic faith.
"Do not imagine that this problem is solely an Iraqi problem, because the terrorist front represents a threat to all free countries and free people of the world," al-Maliki said.
Baghdad's religiously mixed communities such as Karradah have become the focus of sectarian violence. U.S. officials believe control of the capital, the political, cultural, transport and economic hub of the country, will determine the future of Iraq.
Much of the violence has occurred in greater Baghdad in what U.S. officials have described as a "must-win" battle between militants and the new government for the future of Iraq.
The United Nations reported last week that about 6,000 people were killed in Iraq in May and June.