Unknown armed men on Tuesday morning around 10:30 local time opened fire and killed two people and injured a child in the capital city of Khost.
According to the provincial police chief, Mohammad Dawood Amin, the dead were both civilians and did not hold any government posts.
But he continued that one of the victims was a former member of the military.
A police investigation was underway, he said.
No individual or armed group claimed responsibility.
The attack comes amid a spike in targeted killings across the war-torn country.
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