Scores of demonstrators had blocked the highway between the provincial capital of Jalalabad and a major border crossing with Pakistan in protest over the appointment of a local police chief when the suicide bomber blew himself up.
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. They were taken to hospitals in the city of Jalalabad.
There has been no claim of responsibility for any of the attacks, but the Taliban and the Islamic State (IS) group are active in Nangarhar.
The bombs were reportedly hidden inside the schools as part of the planned attack.
He said the protestors asked for dismissal of Bilal Pacha, a commander of local police force members in Achin district, an area close to Mohmad Dara district.
A minimum of 50 people died in a bomb explosion in Afghanistan's eastern Nangarhar province on Tuesday, TOLONews channel reported in Twitter quoting a deputy president of the provincial Council.
Taliban insurgents in a statement posted on their website denied any involvement in the attack.
The intensified fighting has also fuelled speculation over whether Afghanistan's long-delayed parliamentary elections will go ahead on October 20.
"The deadly suicide attack came hours after multiple bombings targeted schools in Jalalabad".
Reports earlier on Tuesday spoke about a chain of explosions near three schools in Nangarhar.
Two air strikes in Baghlan province on Tuesday followed six the day before and American advisers were on the ground supporting Afghan troops, the spokesman added. In January, a Taliban-claimed suicide bombing in the capital Kabul killed at least 103.