The death toll from a suicide attack on a protest gathering in eastern Afghanistan has soared to 68, officials said.

Another 165 were wounded in the September 11 blast in the province of Nangarhar, Attaullah Khogyani, spokesman for the provincial governor said.

The Nangarhar health department confirmed that the death toll from the suicide attack has risen to 68, up from 32, the broadcaster Tolo News reported.

The attack took place on the main highway between the provincial capital, Jalalabad, and the Torkham border crossing with Pakistan.

Khogyani said it targeted a gathering to protest against the appointment of a local police chief and that hundreds of people were present when a suicide attacker detonated explosives.

The attack came hours after smaller bombs targeted at least three schools in and around Jalalabad, killing a boy and wounding four people.

There was no immediate claim of responsibility for any of the bombings, which came as Americans were set to mark the 17th anniversary of the September 11, 2001, terror attacks in New York and Washington.

In a statement, President Ashraf Ghani strongly condemned the suicide attack against the demonstrators and the bomb blasts near the schools, saying that "attacks on civilian facilities, mosques, women, children, are all crimes against humanity."

The UN Assistance Mission in Afghanistan also condemned the series of bombings, and expressed its "mounting concern at the pattern of attacks targeting civilians and schools" in Nangarhar and its capital.

The statement said Nangarhar had seen an "increased spate of threats and attacks" against schools by militants fighting against the Western-backed government since June in retaliation for operations by pro-government forces in the area.

Jalalabad has been in recent months the scene of multiple suicide bombings and attacks that have killed dozens of people.

Both the Taliban and the extremist group Islamic State are active in the area.

Afghan government forces have struggled to counter attacks from both the Taliban and the IS group since the withdrawal of most NATO combat troops in 2014.

With reporting by Reuters, AP and AFP