The attacks were the latest attempts by insurgents to disrupt U.S.-backed efforts to build a strong Iraqi police force capable of taking over security in many towns and cities ahead of nationwide elections slated for January.
An al Qaeda-linked group headed by Jordanian militant Abu Musab al-Zarqawi claimed responsibility for the car bomb, which exploded by a bustling row of shops and cafes and left a gaping 10-foot crater.
Elsewhere, clashes between U.S. troops and insurgents in the western city of Ramadi left at least eight people dead and 18 wounded.
Ramadi is a predominantly Sunni Muslim city where anti-American sentiments are high and U.S. troops and bases in the region come under almost daily attacks. At least one U.S. Humvee could be seen burning as a result of the clashes.
In other developments:
Two American soldiers were killed and three others wounded when they came under attack from an improvised explosive device and small arms fire in Baghdad on Monday at around 4:30 p.m.
On Tuesday, one Task Force Olympia soldier was killed and five were injured when their patrol was attacked with small arms fire in the northeastern city of Mosul.
At least 1,009 American soldiers have died in Iraq, more than 760 of them in hostile action, according to the Pentagon.
The Baghdad blast devastated buildings and gutted cars near the western Baghdad police headquarters on Haifa street, an insurgent enclave that has been the scene of fierce clashes with U.S. troops. Though the attack apparently targeted police, many of the 47 dead were people who had been shopping or having a morning meal.
Paramedics and residents picked up body parts scattered across the street and put them into boxes. Anguished men lifted bodies burned beyond recognition and lay them gently on stretchers. Helicopters circled.
At least 114 were wounded, Health Ministry spokesman Saad Al-Amili said. Hours later, another explosion echoed across the capital, but the blast was caused by an accident involving gasoline street-side vendors, police said. There was no word on casualties.
The bomb was inside a Toyota vehicle parked near the market and a short distance down the road from the police headquarters, which was closed to traffic, said Interior Ministry spokesman Col. Adnan Abdel-Rahman.
Mahdi Mohammed, 30, was standing outside his barber shop when the explosion went off.
"It was a horrific scene. Seconds earlier people were drinking tea or eating sandwiches and then I could see their remains hanging from trees," he said. "I could see burning people running in all directions."
Angry crowds of young men pumped their fists in the air and denounced President Bush and interim Iraqi Prime Minister Ayad Allawi, saying they had failed to protect Iraqis. "Bush is a dog," they chanted.
Others, however, directed their anger at the militants.
"Such acts cannot be considered part of the resistance (against American forces). This is not a jihad, they are not mujahedeen," said Amir Abdel Hassan, a 41-year-old teacher. "Iraq is not a country, it's a big graveyard," he said.
Al-Zarqawi's Tawhid and Jihad group claimed responsibility for the attack in a statement posted on an Islamic Web site. "Thanks to God alone, a lion from the Brigades of Those Seeking Martyrdom succeeded in attacking the center of volunteers for the renegade police apparatus," said the statement, signed by the group.
In Baqouba, gunmen in two cars opened fire Tuesday on a van carrying policemen home from work, killing 11 officers and a civilian, said Qaisar Hamid of Baqouba General Hospital.
The incident occurred when the policemen were returning to their station after they were told that a trip to a training camp has been postponed, said an officer, speaking on condition of anonymity.
Attacks on Iraqi security forces and police officers — seen as collaborators by militants — have left hundreds of people dead since insurgents began a 17-month campaign to expel U.S.-led forces and destabilize Allawi's government.
From April 2003 to May 2004, 710 Iraqi police were killed out of a total force of 130,000 officers, authorities said. Until then, police say, an officer's death was nearly always of natural causes.