Interior Ministry spokesman Najib Danish said the cause of the explosion was a auto bomb in the city's Qabl Bai area.
The comments come a month after the Taliban claimed responsibility for an attack in which an ambulance packed with explosives blew up in Kabul, killing around 100 people, in the worst attack seen in months.
A auto bomb detonated near a passing Australian embassy convoy in eastern Kabul on Friday, an embassy statement said, killing at least one child and wounding several people just days after Afghanistan unveiled plans for Taliban peace talks.
He made the statements in a Farsi interview with ICANA, referring to last week comments by Alice Wells, the Principal Deputy Assistant Secretary in the US State Department's Bureau of South and Central Asian Affairs, that the "door is open" for talks with the Taliban.
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Camera IconSecurity forces inspect the site of an attack in Kabul, Afghanistan, Friday, March 2, 2018.
Additionally, 22 people were injured.
The interior ministry, which gave a higher figure of 22 wounded, said the one fatality had been a 12-year-old boy.
The one killed was a child, a security source and witnesses at the scene told AFP, with the security source adding that more than one dozen people had been injured.
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Lt. Gen. Nasser Khan Janjua, Pakistan's national security advisor, conveyed a message to the Afghan Ambassador to Pakistan Omar Zakhilwal: "Pakistan welcomed President Ghani's offer of seeking peace through dialogue and we are ready to extend all possible support to bring peace in Afghanistan", the Pakistan daily The Nation reported today.
"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. They have not yet offered a full response to the president's proposal, but the apparent openness to negotiations on both sides has sparked cautious optimism.
Since November, the U.S. military has increased air strikes against Taliban positions, training camps and heroin laboratories, which are an important source of revenue for the group.
After 17 years of guerrilla conflict and several diplomatic false starts, American officials take nothing for granted - and they still expect the spring thaw to herald more fierce fighting.
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Security in the capital has been tightened amid fears of more attacks.