Those killed were behind two major attacks in late September including girls at an educational center, says a Taliban spokesperson.
Taliban security forces have reportedly killed six Daesh members in an overnight operation in the Afghan capital, Kabul.
The Daesh fighters killed in the raid on their hideout were involved in two major attacks in recent weeks, Qari Yusuf Ahmadi, a spokesman for the ruling group's administration, said on Saturday.
"They were the attackers of the Wazir Akbar Khan mosque and also ... of Kaaj Institute," said Ahmadi, who said one Taliban security force member was killed in the operation.
No group claimed responsibility for either attack.
The blast at the female section of the Kaaj Institute education centre on September 30 killed 53 people, most of them girls and young women.
On September 23, at least seven people were killed and more than 40 wounded in a blast near a mosque in Wazir Akbar Khan, a heavily fortified neighbourhood once home to a "Green Zone" of embassies and foreign force bases.
READ MORE: Deadly blast targets mosque near Afghan interior ministry in Kabul
Series of blasts
Since the Taliban took over in 2021, they say they have focused on securing the country after decades of war.
However, a series of blasts have rocked the capital and other urban areas in recent months and the United Nations has said security is deteriorating.
The Afghan affiliate of Daesh known as Daesh-K, named after an old name of the region (Khorasan), are enemies of the Taliban.
Fighters loyal to Daesh first appeared in eastern Afghanistan in 2014, and later made inroads in other areas.
READ MORE: Afghans protest after dozens killed in Kabul college attack