Khogyani said the suicide bomber detonated his vest as he approached a tent where protesters had gathered.
The bombs were reportedly hidden inside the schools as part of the planned attack.
After seizing a military base in Sar-e-Pul, Taliban fighters were closing in on the provincial capital in a situation that could result in "disaster" if reinforcements were not sent, the area's police chief Abdul Qayom Baqizoy warned on Monday.
According to a united Nations report published in mid-July, the number of civilians killed in Afghanistan in the first six months of the year reached a record high of almost 1,700 dead, due in majority to the attacks of the AES, the worst record in ten years, according to the UN.
The attack comes amid surge of strikes by the Islamic State and Taliban insurgents elsewhere in the country since last week in which more than 200 people have been killed.More news: Mets' David Wright To Play One More Game Before Retiring
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The latest toll, reported by Attaullah Khogyani, a spokesman for the provincial governor, was up from an earlier figure of 32, according to The Associated Press. They were taken to hospitals in the city of Jalalabad.
Violence across the country has intensified in recent weeks as the Taliban make gains on the battlefield and IS launches deadly urban attacks.
The death toll from Tuesday's blast soared overnight. That blast was later followed by two others in Behsud district, also near two schools.
The escalating violence has dampened hopes of peace talks to end Afghanistan's 17-year conflict but two Taliban officials on Tuesday told Reuters the movement was preparing for another meeting with USA officials following one in July.
There were no reports of U.S. strikes in Sar-e Pul on Tuesday but there were three strikes on Monday, a spokesman for U.S. forces in Afghanistan said in an emailed statement. AFP said an explosion near a school in Jalalabad, the capital of the province, killed a boy and left four adults injured.