Nine children were among 12 people killed when a suicide bomber blew up a truck in the northern Iraqi city of Kirkuk, police say.
Emergency departments were overwhelmed with injured people
A further 192 people were injured in the blast, which happened when a bomber drove a truck laden with explosives into a barrier at a police station.
Many of the victims were children from a nearby primary school, police said.
In other violence, the handcuffed bodies of 19 workers kidnapped north of Baghdad have been found.
In Kirkuk, police said the attacker rammed concrete barriers surrounding the police criminal investigation department and detonated explosives hidden under a load of flour.
The building was partially destroyed and the blast was heard across the city, reports said.
Hospitals were said to be overrun with the injured, many of them school children.
"We were at the last lesson and we heard the explosion," schoolgirl Naz Omar told the French news agency AFP.
"I saw two of my class mates sitting near the window. They fell on the floor, drenched in blood."
Some reports suggested US troops had been injured in the blast, but there was no immediate confirmation from US military authorities.
In Baghdad, the bodies of 19 Shia workers from the city's Shorja market were found.
The workers were kidnapped on Sunday at a fake checkpoint, officials said. Gunmen stormed their minibus as they returned home to the restive northern province of Diyala.
The bodies were found handcuffed and blindfolded near a water treatment facility in Morariyah village, police said. All had died from gunshot wounds to the head, hospital officials said.
Meanwhile, US Senator and presidential hopeful John McCain, who is leading a congressional delegation to Baghdad, has insisted the US-Iraqi security crackdown there is working.
He told a news conference on Sunday that there were "encouraging signs".
"I've been here ... many times over the years. Never have I been able to drive from the airport, never have I been able go out into the city as I was today," he said.
But he said there was a long way to go.
"I believe that the signs are encouraging, but please don't interpret one comment of mine in any way to indicate that this isn't a long, difficult struggle."
Six US soldiers were killed in roadside blasts south of Baghdad at the weekend.
Iraqi figures estimate civilian deaths caused by violence across the country rose by 13% in March - to 1,861 - despite the security crackdown in Baghdad.