Those among the killed were five women and five children.
On Thursday night, five police personnel were killed in an insider attack in Ghanikhel district in Nangarhar province of the country.
Those killed by the roadside bomb in Logar province - five women, five children and a man - were all from the same family, said Salim Salleh, spokesperson for the provincial governor of Logar.
At least 113 militants were killed and 50 injured when Afghan security forces pressed ahead with offensives in restive provinces, the Defence Ministry said on Friday.
Man who ran over pedestrians was 'hearing voices'
The New York Police Department says the driver drove along the sidewalk for at least three blocks, hitting pedestrians as he went. A woman who used to live in the building, Fati Razak, said she occasionally sees Rojas when she returns to visit her mother.
He added that after the shootings, the attacker, whose name was only given as Nasratullah, collected his victims' firearms and fled the scene.
Neither the Taliban nor the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) - the two armed groups who operate in the area - immediately claimed responsibility for the attack in Nangarhar, a mountainous province that borders Pakistan.
There was also no claim of responsibility for the attack in Logar, but Salleh accused the Taliban of planting the roadside bomb.
Hours earlier on Friday, a roadside bomb hit an American military convoy north of the capital, Kabul, but "no injuries have been reported", said the USA military.
In the first four months of 2017, some 987 child casualties were reported from conflict-related incidents - a record high for the period since the United Nations began documenting such cases.