The bomb struck a bus travelling through Kandahar province. The attack is said to the third since a brief ceasefire declared by the Taliban for a major Muslim holiday that ended last month.
The blast targeted Wazir Akber Khan Mosque in Kabul when worshipers had gathered for evening prayers, according to Afghan's interior ministry official.
The attacks come on the heels of a rare three-day truce during the Eid al Fitr holiday that ended on Tuesday night.
US and NATO officials said that US troop strength in Afghanistan is down to nearly 8,600, well ahead of a schedule agreed with Taliban in late February, in part because of concerns about the spread of the coronavirus.
US President Donald Trump says his country should no longer be a police force in Afghanistan after 19 years, calling for troop withdrawal, which according to reports is considerably ahead of schedule.
The Taliban-claimed attack, which targeted a base in eastern Afghanistan belonging to the country's intelligence service, also wounded at least 40 people and left eight others in critical condition.
The Taliban-claimed blast comes after President Ashraf Ghani had ordered the military to launch action, drawing a line under the defensive stance it adopted as the US withdraws troops and tries to broker talks with the Taliban.
No one has claimed responsibility for the attack yet and the Taliban denied any involvement.
Interior Ministry spokesman Tariq Arian says bomber detonated his explosives among civilians in Reshkhor area of Afghanistan's capital.
The attack on Bagram airfield was carried out from a vehicle parked in an adjoining village.
The Afghan government and militant group have been negotiating in Kabul since last week but finalising a prisoner swap has been beset with problems. Meanwhile, at least seven civilians were killed in a Taliban attack in Balkh, local officials said.
Meanwhile, President Ashraf Ghani has announced his new Cabinet even as he squabbles with his main political challenger over last year's election results.
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