A spokesman for the Interior Ministry said the attack targeted a convoy of foreign forces in the Qabel Bai area in Kabul's PD9, which is home to a military training center, the report said.
Kabul has recently seen a spate of large-scale militant attacks by the Taliban and also the Islamic State group, whose affiliate in Afghanistan has grown stronger since it emerged in 2014.
A auto bomb exploded near Australian Embassy vehicles in Kabul on Friday, killing an Afghan child.
No Australians were injured in the attack, the Department of Foreign Affairs says.
An Afghan security personnel gestures as he arrives at the site of a vehicle bomb attack targeting a foreign forces, in Kabul on March 2, 2018.
The interior ministry, which gave a higher figure of 22 wounded, said the one fatality had been a 12-year-old boy. North Atlantic Treaty Organisation forces in Kabul confirmed the attack was a suicide auto bombing.
It was first thought no Australians were injured in the attack on Friday, but Foreign Minister Julie Bishop has confirmed two suffered minor injuries.
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However, a security source told TOLOnews that three people were killed in the explosion.
The attack came two days after President Ashraf Ghani offered to start peace talks with the Taliban, and just over a month after an ambulance packed with explosives was detonated in the city centre, killing about 100 people.
"We fully endorse President Ghani's call for the Taliban to join the peace process", Gresback, the North Atlantic Treaty Organisation spokesman, said in his statement.
As part of its new regional strategy announced a year ago, the United States has stepped up assistance to the Afghan military and greatly increased air strikes against the Taliban, in a bid to break the stalemate and force the insurgents to the negotiating table.
"We reinforce our call to the Taliban to begin direct talks with the Afghan government with no preconditions", Bass said.
The Taliban "calls on American officials to talk directly to the Political Office" of the group, read the statement, apparently referring to an alleged office in the Qatari capital.