Meanwhile, early Friday, U.S. and Iraqi forces launched a major attack against the insurgent stronghold of Samarra, securing government and police buildings in the city, the U.S. command said.
In the wake of Thursday's bombings, grief-stricken mothers wailed over their children's bloodied corpses, as relatives collected body parts from the street for burial and a boy picked up the damaged bicycle of his dead brother.
The wounded were rushed to Yarmouk Hospital, where angry relatives screamed for attention from the overwhelmed doctors, many of whom wore uniforms covered in blood. One woman tore at her hair before pulling back the sheet covering her dead brother and kissing his body.
The bombings in Baghdad's western al-Amel neighborhood at least two of which were in cars came amid a series of savage attacks that killed at least 51 people and wounded 230 nationwide. At least one U.S. soldier was among the dead and 13 were wounded.
On Friday, the joint offensive came in response to "repeated and unprovoked attacks by anti-Iraqi forces" against Iraqi and coalition forces, the military said in a statement. Its aim was to kill or capture insurgents in the city, 60 miles north of Baghdad.
The statement provided no further details of the fighting. A report by CNN said 2,000 rebels were believed to be holed up in the city and that tanks and jets were being used as troops took the city "sector by sector."
Jordanian terror mastermind Abu Musab al-Zarqawi's Tawhid and Jihad group claimed responsibility for bloody attacks in Baghdad on Thursday, according to a statement posted on a militant Web site.
The authenticity of the statement could not be verified, and it was unclear whether the three "heroic operations" it cites attacks on a government complex and "a convoy of invading forces" included the bombs that killed the children.
Early reports said a U.S. convoy was passing by the celebration when the attack occurred. The U.S. military said later that American soldiers were taking part in the celebration but that no convoy was passing through the area.
Deputy Interior Minister Gen. Hussein Ali Kamal said intense military pressure on insurgents holed up in Fallujah, west of Baghdad, was forcing them to turn their bombs on the capital. He said the day's attacks were "definitely coordinated."
"They are killing citizens and spreading horror. They have no aims except killing as many Iraqis as they can," Kamal told The Associated Press. American jets, tanks and artillery units have repeatedly targeted al-Zarqawi's followers in Fallujah, as coalition forces seek to assert control over insurgent enclaves ahead of elections slated for January.
After the bombings at the government-sponsored celebration in the capital, Yarmouk Hospital received 42 bodies, including 35 children, said Dr. Azhar Zeid. The hospital also treated 131 wounded, 72 of them under age 14, added Dr. Mohammed Salaheddin.
Some of the children, who are near the end of a nationwide school vacation, said they were attracted to the neighborhood celebration by American soldiers handing out candy.
"The Americans called us. They told us: 'Come here, come here,' asking us if we wanted sweets. We went beside them, then a car exploded," said 12-year-old Abdel Rahman Dawoud, lying naked in a hospital bed with shrapnel embedded all over his body.
Interior Ministry spokesman Col. Adnan Abdul-Rahman said a car bomb and an explosive device planted in the road detonated in quick succession at the site of the celebration. Soon afterward, a second car bomb plowed into the area as crowds rushed to help the wounded, he said.
Maj. Phil Smith, spokesman for the U.S. 1st Cavalry Division, said all three blasts were caused by car bombs, the first two targeting the celebration and the third aimed at an Iraqi National Guard checkpoint about a mile away. Ten U.S. soldiers were wounded, he said.
Neither official would confirm whether suicide attackers were involved, and the conflicting accounts could not immediately be reconciled.
"This attack was carried out by evil people who do not want the Iraqis to celebrate and don't want (reconstruction) projects in Iraq," National Guard Lt. Ahmad Saad said at the scene.
Hours earlier, a suicide attacker detonated a vehicle packed with explosives in front of a government complex in the Abu Ghraib area, on the western outskirts of Baghdad. The bombing killed a U.S. soldier and two Iraqi policeman and wounded more than 60 people, including three American soldiers.
U.S. forces guard the compound, which houses the mayor's office, a police station and other buildings, police 1st Lt. Ahmed Jawad said.
"I saw people flying in the air and falling on the ground," said Saad Mohsin, who has a table in front of the mayor's building where he helps people fill out forms. "I had fragments in my neck and my back."
Distraught relatives searched the damaged buildings, calling for missing loved ones. Others gathered outside the hospital hoping for news.
Policeman Ali Shihan was hit by shrapnel in his left ear and was covered in blood.
"Those terrorists have no goal except killing Iraqis," he said.
Iraqi Foreign Minister Hoshyar Zebari said he was disturbed by the televised images of the day's attacks, which he said showed the importance of training Iraqi military and security forces and improved intelligence gathering.
"The Iraqi people have suffered enough at the hands of these people," Zebari said on CNN, speaking from London. "We want a new Iraq, a different Iraq."
Also on Baghdad's outskirts, insurgents fired a rocket Thursday at a logistical support area for coalition forces, killing one soldier and wounding seven, the U.S. military said. No further information was disclosed including the nationalities of the victims.
In the northern city of Tal Afar, a car bomb targeting the police chief killed at least four people and wounded 19, including five policemen, police and hospital officials said. The police chief escaped unharmed.
In another northern city, the Kirkuk mayor's chief bodyguard was gunned down in his vehicle, which the attackers then drove away, police said.
Early Thursday, U.S. forces struck a suspected militant safehouse in Fallujah. Hospital officials said at least four Iraqis were killed and eight wounded.
"Significant secondary explosions were observed during the impact indicating a large cache of illegal ordnance was stored in the safehouse," the military said in a statement.
Thursday's violence came as the Arab news network Al-Jazeera showed footage of 10 new hostages seized in Iraq by militants seen pointing guns at them. They included six Iraqis, two Lebanese and two Indonesian women, Al-Jazeera reported. It was not clear when or where they were seized.
Militants calling themselves The Islamic Army in Iraq claimed responsibility for the kidnapping. There was no mention of any demands. The group also says it is holding two French journalists.
Nearly 150 foreigners have been kidnapped in Iraq and at least 26 have been killed. Some were seized by insurgents as leverage in their campaign against the United States and its allies, others by criminals seeking ransom.
Associated Press Writers Sameer N. Yacoub and Sinan Salaheddin contributed to this report.