In the Laghman province, a Taliban mortar round struck a house, killing two women and wounding three children, said Sarhadi Zwak, a spokesman for the Laghman governor.
No one immediately claimed either attack, but the officials blamed both on the Taliban.
The Interior Ministry meanwhile said Afghan forces retook a district from the Taliban in the northern Kunduz province amid fierce clashes. The Qala-e-Zal district fell to the Taliban earlier this month after insurgents overran the local police headquarters.
Elsewhere in Afghanistan, 12 Islamic State fighters in the eastern Nangarhar province agreed to hand over their weapons and join a government-backed peace process on Monday, according to Ataullah Khogyani, a spokesman for the provincial governor.
An Islamic State affiliate in eastern Afghanistan has expanded its reach in recent years, battling both the US- backed government and the larger and more entrenched Taliban.
The two extremist groups are committed to establishing a harsh version of Islamic rule, but are bitterly divided over leadership and tactics.