The battle was over once the Afghan security forces killed the assailants.
At least four attackers armed with rocket-propelled grenades and machine guns were fighting police, he said.
Daesh has claimed responsibility for an attack on a government building in Afghanistan on Sunday, the militant group's Amaq news agency said without providing any evidence.
Security forces were able to rescue around 50 employees stuck in the building during the attack, he added.
At least nine people, including a child, had been killed and 36 wounded, public health officials said.
Earlier, he said there had been two explosions.
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The capital of Nangarhar Province is near to the Pakistan border.
April saw a series of attacks across the country targeting voter registration centres as Afghanistan gears up for long-delayed legislative elections due in October.
The Taliban have seized control of districts across the country, and the two groups have carried out attacks in the Afghan capital, Kabul, in recent months that killed scores of people.
The Taliban recently launched their annual spring offensive, in an apparent rejection of a peace overture by the Afghan government.
Their Operation Al Khandaq will target USA forces and "their intelligence agents" as well as their "internal supporters", a Taliban statement said on April 25. Some areas of the province are a stronghold of the ISIS group but Taliban fighters are also active there.
Heavy security forces arrived at the spot of the attack.