Five people were killed and 38 others wounded on Monday in fighting between Taliban militants and security forces, the public health ministry said.
The death toll did not include four militants who were also killed during the attacks, which lasted more than three hours.
"We have five martyred and 38 wounded," Sayed Kabir Amiri, head of hospitals at the ministry of public health said.
"These figures have been reported from all hospitals in the city. The dead include civilians and security personal. The wounded are mostly civilians."
Officials in Kabul have said they were clearing buildings that were taken over by Taliban militants, though an interior ministry spokesman said there was still some "resistance".