Two bombs went off at a village near the city of Tal Afar in the northern province of Nineveh, killing at least 15 people and injuring 122 others, said Aal al-Abbasi, a government official.
The explosions caused the partial collapse of an elementary school in the village of Qabat, near the Syrian border, Voice of America reported.
"The reports said that a total of five policemen, school principal and nine school children were killed and 122 people were wounded in the two suicide car bombs near a school and a police station in the village of Qabat," he said.
Most of the wounded were school children, many of whom were in critical condition, he added.
Authorities said they feared more children were trapped in the rubble.
Another bomber blew up his suicide vest among a crowd of Shiite pilgrims in the Seliekh district in northern Baghdad, killing 12 people and injuring 25, Chinese state-run news agency Xinhua reported.
That attack came as pilgrims processed to commemorate the death of Imam Mohammed al-Jawad, whose tomb is located in the holy Shiite Kadhimiya district.
On Saturday, another suicide bomb killed 51 of the pilgrims and injured 107 others outside a mosque in the same neighborhood.
No group had claimed responsibility for the attacks.
On Saturday, at least 78 people died and 166 were wounded in attacks across Iraq, Xinhua reported.
Also in Baghdad on Saturday, 11 people died and 35 others wounded when a car bomb exploded near a popular cafe, police said. A second car bomb killed a police officer and wounded two others in southwestern Baghdad and a third car bomb killed one civilian and injured 10 others.
A bomb also killed a government employee in Baghdad, police said.
At a joint army and police checkpoint outside the town of Fallujah, a gunman killed a soldier and a policeman and injured two other soldiers, police said.
At a security checkpoint in Yousifiyah, a roadside bomb killed three paramilitary fighters and wounded four others, police said.
Gunman also carried out attacks in the cities of Mosul, Hawijah, and the Amriyat al-Fallujah area, killing a total of six people and injuring five others.