One attack appeared to have targeted an office of Afghanistan's intelligence agency on the outskirts of Kabul, they said.
A gunbattle broke out between security forces and an unknown number of gunmen immediately after a resounding explosion in the western part of Kabul, a police official said.
Fighting was concentrated near a district police headquarters located not far from a military training school, said the official, who spoke on condition of anonymity because he was not authorized to talk to the media.
There was no immediate official comment from police, and no word on casualties.
The explosion was large enough to be heard on the other side of the city. Last month, a suicide bomber killed at least 20 people outside the Supreme Court in Kabul. Militant group Islamic State claimed responsibility for that attack.