Relatives say three girls and a boy were walking to school when they were killed on Wednesday.
At least 19 other people, including six police officers, died in car bombings and shootings across the Iraqi capital.
The violence took place as Iraqi leaders try to hammer out deals in advance of the formation of the country's next government, which the US sees as its best chance to restore security and reduce its troop numbers in the country.
The children killed in the bombing in central Baghdad's bustling Fadel district were 10- to 14-years old and included two daughters and a son of Jamil Mohammed, a struggling vendor who works in a nearby public market.
Mohammed said: "We are poor people who have nothing to do with politics.
"We only wanted to live a decent life. What is the guilt of my dead children? They were only heading to school. Now I am left with only two children. This is a disaster for my family."
The bombing took place outside a camera shop that sold black market alcohol and damaged several other stores, police Lieutenant Ali Mittab said.
A woman grieves at the site
where the schoolchildren died
It was unclear whether the shop was the target or nearby police patrols.
At least three car bombs exploded across the capital on Wednesday, targeting police but killing and injuring ordinary Iraqis as well.
A parked car bomb exploded as a police patrol passed, killing four police officers and wounding two civilians in northern Baghdad, said Lieutenant Nadhim Nasser.
Another car bomb blast killed two civilians near Baghdad's University of Technology, according to Jabir Mohammed of the eastern Baghdad emergency services department.
Five people were wounded, three of them police, he said.
A third explosives-rigged vehicle blew up near a petrol station as an Iraqi police patrol passed in downtown Baghdad's Karradah area, wounding five police officers and three civilians, Major Abbas Mohammed said.
Armed men firing from two cars shot and killed police Captain Hussein Ali Youssef and his driver, also a police officer, in southwestern Baghdad's Sadiyah neighbourhood, police Lieutenant Aqil Fadil said.
Also on Wednesday, gunmen killed three people including a blacksmith at his Sadiyah workshop, another man who opened his door in the southern Dora neighbourhood and a civilian driving in western Baghdad's Ghazaliyah district.
Police said they found the bodies of five men on Wednesday shot in the head and dumped near a Shia neighbourhood of western Baghdad.
Their identities were unknown but they appeared to be the victims of sectarian tit-for-tat killings that have swept the capital for months.
US soldiers killed five insurgents within 24 hours, including one in a shootout fought south of Baghdad early on Wednesday, the military said.
Bird flu alert
Iraqi authorities, meanwhile, have declared a bird flu alert in the southern province of Maysan and called for security forces to prevent people from carrying birds in and out of the area, health officials said on Wednesday.
Shanjin Abdel Qader, 14, was the
first victim of bird flu in Iraq
The alert is the latest measure taken by Iraqi health authorities to combat the deadly H5N1 bird flu strain after last month's discovery of the country's only confirmed case of the disease in a human.