Separately on Thursday, Islamic State also claimed responsibility for a suicide bombing in Kabul that tore through an educational center on Wednesday where teenagers had been studying for a university entrance examination.
The United Nations Security Council condemned the bombing as a "heinous and cowardly terrorist attack", saying that it "underlined the need to hold perpetrators, organizers, financiers and sponsors of these reprehensible acts of terrorism accountable and bring them to justice".
"UNICEF is gravely concerned about the growing violence across Afghanistan, especially over the past week, where children continue to be the hardest hit", UNICEF Executive Director Henrietta Fore said in a statement. It said 57 people were wounded in the bombing, part of spate of attacks against a branch of Islam that the Islamic State considers heretical.
In addition to the IS attacks, Taliban militants also delivered high-profile, demoralising blows in the strategic city of Ghazni - which they attacked last week, forcing security forces backed by USA air power to struggle for days to push them out - and in Faryab, where they captured a northern base, killing at least 17 soldiers.
There was no immediate word of a claim of responsibility, but Taliban spokesman Zabiullah Mojahid denied that the group was to blame.
Dilawar Aymaq, a parliamentarian from Baghlan, said the attack targeted a military checkpoint and another manned by the so-called local police, militias recruited and paid by the Interior Ministry. That assault began last Friday.
On Tuesday, the AP says, the Taliban killed 17 soldiers in northern Faryab province after besieging an army base for several days. Afghan forces repelled the initial assault and in recent days have struggled to flush the insurgents out of residential areas where they are holed up. "So, I believe the Taliban do not believe in peace talks", said shopkeeper Shahenshah Shahin in Kabul.
The surge in violence comes just weeks after Afghans marked an unprecedented country-wide ceasefire between the Taliban and government forces in June, giving some temporary relief to civilians.
Numerous dead were security forces, he said, adding that many more had been injured, as fighting continued despite government and U.S. assurances that the assault had failed.
Separately, six girls younger than 10 were killed when an unexploded mortar they picked up to play with suddenly exploded on Wednesday, officials in the eastern province of Laghman said.
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