The bomber who was on foot targeted a bus carrying Afghan troops in Tangi Tarakhil on the outskirts of the capital, Kabul Crime Branch Unit chief General Farid Afzail told AFP.
Taliban spokesman Zabihullah Mujahid claimed responsibility for the attack in a message sent to the media.
"Around 7:15 am, a suicide bomber on foot targeted a bus of Afghan Army soldiers in Tangi Tarakhil area of Kabul city," Afzail said.
Kabul has been hit by a spate of deadly attacks in recent weeks, heightening concerns that Afghanistan could tip into a spiral of violence as the US-led military presence declines.
NATO's force in Afghanistan will change on December 31 from a combat mission to a support role, with troop numbers cut to about 12,500 -- down from a peak of 130,000 in 2010.
Militants have targeted foreign guest houses, embassy vehicles, US troops and Afghan army buses in Kabul over the past month, undermining claims that the insurgency is weakening as NATO's 13-year war ends.
He said Afghanistan's newly-elected government and its security forces were ready to take charge of security.
Hagel insisted Afghanistan would not go the way of Iraq, where another US-trained army virtually collapsed in the face of an onslaught by Islamic State jihadists after American troops left the country in 2011.
But a day later, Afghanistan's chief executive Abdullah Abdullah told Britain's Sunday Times newspaper that Western forces were leaving prematurely.
"Two years ago we had 150,000 international troops and lots of jets and helicopters. Within two months there will be just 12,000. We need air support for the medical evacuation of casualties, intelligence and fast jets.
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