The attacks are the latest in a relentless wave of killing that has made for Iraq's deadliest outburst of violence since 2008. The mounting death tolls are raising fears that the country is falling back into the spiral of violence that brought it to the edge of civil war in the years after the 2003 U.S.-led invasion.
Sunday's blasts began around 9:30 a.m. in the Shiite Turkomen village of Qabak, just outside the town of Tal Afar. The area around the stricken village has long been a hotbed for hard-to-rout Sunni insurgents and a corridor for extremist fighters arriving from nearby Syria.
One car bomb in the tiny village targeted an elementary school while children ages 6 to 12 were in class as another struck a nearby police station, Tal Afar mayor Abdul Aal al-Obeidi said.
The dead included 12 children, the school principal and two policemen. Another 90 people were wounded, he said.
The village is home to only about 200 residents, and part of the single-story school collapsed as a result of the blast, he said. Tal Afar is 420 kilometers (260 miles) northwest of Baghdad.
"We and Iraq are plagued by al-Qaida," al-Obeidi said. "It's a tragedy. These innocent children were here to study. What sins did these children commit?"
Another suicide bomber, this time on foot, blew himself up hours later as Shiite pilgrims walked through the largely Sunni neighborhood of Waziriyah in the north of the Iraqi capital.
At least 12 people were killed and 23 wounded in that attack, according to police and hospital officials. They spoke on condition of anonymity because they weren't authorized to brief reporters.
It was the second time in less than 24 hours that a suicide bomber managed to thwart security checkpoints and target Shiite pilgrims making their way to a golden-domed shrine in northern Baghdad where two revered Shiite saints are buried.
A suicide bombing in the largely Sunni neighborhood of Azamiyah, not far from the site of Sunday's attack, late Saturday killed 51, authorities said as they revised the death toll upward. That and other attacks Saturday left a total of 75 dead.
There was no immediate claim of responsibility, but suicide bombers and car bombs are frequently used by al-Qaida's Iraq branch. It often targets Shiite civilians in an effort to undermine the Shiite-led government. Its extremist ideology considers Shiites heretics.
United Nations figures released this week showed that at least 979 people, most of them civilians, were killed last month alone. At least 135 have died violently since the start of October, according to an Associated Press count.
Associated Press writer Adam Schreck contributed.