Stanikzai said locals had gathered to complain about a local police commander and the suicide bomber targeted them.
Officials have said violence is likely to intensify before parliamentary elections next month and a presidential election in April.
The spokesperson said that the third explosion took place in police district number three in the provincial capital of Jalalabad, wounding one civilian. The Taliban denied involvement.
No group has said it carried out the suicide bombing in the crowd of protesters in Nangarhar's Momand Dara district, but Islamic State militants are active in the province.
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In recent days, Taliban fighters killed almost 60 members of the security forces in a spate of attacks in the country's north, and threatened a provincial capital for the second time in as many months. The protest was held in Mohmand Dara district near Jalalabad-Torkham Highway.
In early September, at least 20 people, including two journalists came on the scene, had been killed in a double bombing claimed by the EI for the shi'a community of the capital.
In the northern province of Sar-e Pul, hundreds of armed men assembled to boost the city's defences as security forces fought to push the Taliban back from the city centre, said Zabihullah Amani, the provincial governor's spokesman.
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.
Also in Nangarhar, at least one person was killed and four others wounded in a series of additional bomb blasts near different schools, said Khogyani.