A suicide bomber blew himself up at the entrance of a police station in central Kabul. The area is near foreign embassies and government offices, according to an interior ministry official.
There were three loud blasts in rapid succession according to police and interior ministry officials.
At least six people were injured in back-to-back suicide bombings.
Officials report a "cleanup operation" is underway.
Elsewhere, the Taliban advanced on a compound in the northern Faryab province.
Daesh (also known as ISIS ) terrorists have already claimed responsibility for the attack.
Interior ministry spokesman Najib Danish told "The second attack happened in front of police precinct 10 in Shahr-e-Naw in central Kabul," and added that "two attackers who tried to enter the police compound were shot dead."
An official from a branch of the Afghanistan International Bank who was reached by telephone said, "We can hear the gun shots and we are waiting inside the bank's safe room until the clashes end."
Officials said that at least three suicide bombers attacked police stations in Kabul
Kabul has seen an increase in bombings and other attacks against the security forces and civilians since the Taliban announced the beginning of their spring offensive on April 25.