The blasts in the Afghan capital were heard alongside anti-aircraft weapons and gunfire from across the city, and came as the Afghan defence ministry said "the fighting is still ongoing" against Pakistani forces.
An AFP journalist in Jalalabad city, between Kabul and the frontier, reported hearing explosions and various weapons being fired.
At the nearest border crossing, around 50 kilometres (30 miles) from Jalalabad, residents in Torkham told AFP the days-long fighting was continuing.
The neighbours have clashed along the frontier since Thursday, when Afghanistan launched a border offensive in response to Pakistani air strikes.
The latest casualties include three children killed Monday in a "crime committed by the Pakistani military regime" in Kunar province, Afghan deputy government spokesman Hamdullah Fitrat said.
At least 39 civilians have been killed since Thursday, the Afghan government said, a toll which Pakistan has not commented on.
The UN children's charity said it was "alarmed" by reports of child casualties in the conflict, and called on all sides to "exercise maximum restraint, protect civilian lives".
Islamabad said its February air strikes that sparked the escalation were targeting militants.
Islamabad accuses Afghanistan of failing to act against militant groups that carry out attacks in Pakistan, which the Taliban government rejects.
The border fighting has hit multiple Afghan provinces.
The latest clashes were taking place in southern Kandahar, the defence ministry said, as well as neighbouring Zabul, according to the provincial information department.
The violence of recent days is the worst since October fighting killed more than 70 people on both sides, with land borders between the neighbours largely shut since.
