The attack was one of the worst in Afghanistan for months. No other group immediately claimed responsibility, but both Taliban insurgents and the Islamic State group are active in eastern Afghanistan, especially in Nangarhar province.
It was the deadliest attack since an ambulance packed with explosives detonated in a crowded street in the heart of Kabul in January, killing more than 100 people, mostly civilians.
The peaceful protesters accused a local police officer of misusing power, calling upon the government to sack and punish him when the blast happened, the official added.
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. The wounded were cared for in the corridors, the more seriously ill were transported to the central hospital in Jalalabad.
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Officials have said violence is likely to intensify before parliamentary elections next month and a presidential election in April. The Taliban denied involvement.
Another official Sohrab Qaderi, a member of the Nangarhar provincial council, said at least 56 bodies were taken to hospital, with 43 more wounded.
Tuesday's attack was marked by one of the highest death tolls in attacks in Afghanistan this year.
The explosion at the protest followed a series of smaller blasts on Tuesday that targeted schools in Jalalabad and surrounding districts that were returning after summer breaks. Two other blasts took place in Bihsud district early morning. The provincial governor's spokesman, Attahullah Khogyani, made a statement with a revised casualty total on Wednesday. That bombing was claimed by the Taliban.