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 US-led invasion.
Today's blasts began around 9:30 am 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.
The dead included 12 children, the school principal and two policemen. Another 90 people were wounded, he said.
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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 kilometres northwest of Baghdad.
"We and Iraq are plagued by al-Qaeda," al-Obeidi said. "It's a tragedy. These innocent children were here to study. What sins did these children commit?"
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 authorised 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 Baghdad where two revered Shiite saints are buried.
There was no immediate claim of responsibility, but suicide bombers and car bombs are frequently used by al-Qaeda's Iraq branch.