According to reports, two suicide bombers hit army buses in Kabul in the twin attack, police said.
Taliban militants, claimed responsibility for the early-morning attacks on the buses.
According to initial reports six military men and civilians were killed in the attacks.
The Taliban have claimed the responsibility of the suicide attacks saying it is a clear message to the government that signed the agreement with United States and warning to step up attacks.
United States and Afghanistan on Tuesday signed a bilateral security agreement to allow about 10,000 US troops to stay in the country next year.
Newly-elected President Ashraf Ghani signed this agreement on his first day in office as an initiative to improve relations between Kabul and Washington.