The raids on eight to 10 police posts began early on Sunday, Mr Haji Ghalib, governor of Achin district in Nangarhar province, told AFP, giving no casualty figures.
"This is the first time that Daesh fighters have launched coordinated attacks on police checkpoints in Nangarhar," he said, AFP reported.
Daesh is an Arabic acronym for ISIL, which controls wide swathes of territory in Iraq and Syria.
The attacks in Achin were confirmed by the border police commander in eastern Afghanistan, Mohammad Ayoub Hussainkhail.
They came a day after a United Nations report warned that ISIL was making inroads in Afghanistan, winning over a growing number of sympathisers and recruiting followers in 25 of the country's 34 provinces.
Afghan security forces told UN sanctions monitors that about 10 per cent of the Taliban militants are ISIL sympathisers, according to the report by the UN's Al-Qaeda monitoring team.
The militant group has been trying to establish itself in Afghanistan and challenging the Taliban on their own turf.
Some Taliban members, particularly in the restive eastern provinces of Kunar and Nangarhar, have adopted the ISIL flag to rebrand themselves as a more lethal force.