Scores of people were also wounded in the bombing at the entrance of the base, which left several bodies and charred debris strewn around the area.
The attack comes amid the Taliban's unprecedented winter offensive despite a renewed push to restart formal peace talks.
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"Ten people were reported killed and 20 others were wounded in a suicide attack in Deh Mazang square of Kabul city," deputy interior minister Mohammad Ayoub Salangi said on Twitter.
"Most of the victims were civilians."
Kabul police spokesman Basir Mujahid reported a death toll of nine, adding that as many as 12 people including a woman were wounded.
The health ministry said some of those wounded were hit in the chest by flying shrapnel and are in critical condition.
Ambulances rushed to the scene, which was cordoned off by authorities.
The Taliban claimed responsibility for the attack, with insurgent spokesman Zabihullah Mujahid claiming on Twitter that up to 40 police were killed and wounded.
The militants routinely exaggerate the toll in attacks on the Afghan government.
The carnage comes just ahead of a third round of four-country "roadmap talks" trying to lay the groundwork for direct dialogue between Kabul and the Islamist group.
Delegates from Afghanistan, Pakistan, China and the United States are set to convene in Islamabad on February 6 in a bid to seek a negotiated end to the Taliban insurgency, now in its fifteenth year.
The Taliban have stepped up attacks on government and foreign targets in Afghanistan this winter, when fighting usually abates, underscoring a worsening security situation.
In recent months the Taliban briefly captured the northern city of Kunduz, the first urban centre to fall to the insurgents, and have seized territory in the opium-growing southern province of Helmand.
Observers say the intensifying insurgency highlights a push by the militants to seize more territory in an attempt to wrangle greater concessions during talks.
Pakistan -- the Taliban's historic backers -- hosted a milestone first round of talks directly with the Taliban in July.
But the negotiations stalled when the insurgents belatedly confirmed the death of longtime leader Mullah Omar, sparking infighting within the group.
The first and second round of the four-country talks were held last month in Islamabad and Kabul respectively.
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