A ministry spokesperson said one person was killed in an attack on an office of the main intelligence agency on the city's eastern outskirts, while at least 35 people were wounded in a separate attack on a police office in the west of Kabul.
Earlier, Afghan Taliban militants claimed they attacked police, military and intelligence targets in Kabul.
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.
At least 19 killed in suicide blast at Afghan Supreme Court
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 authorised to talk to the media. 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.
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