It was not immediately clear how the bomber managed to sneak into the building, used by the Shiite community as an education center, in the Dasht-i Barcha area of Kabul.
The injury toll was revised to 56 from 67.
Hossain recounted to The Associated Press how when he entered Fareba's classroom, he saw parts of human bodies all over student desks and benches. "No place is safe for us.' But she said 'No, no, no", the mother said.
The radical Islamist group made the claim on its Amaq news agency, saying the attacker used a suicide vest in the strike Wednesday, which targeted a classroom packed with teenagers in a Shiite Muslim district of the Afghan capital.
According to Kabul police, the assailants used a nearby house under construction to stage the attack, which sparked exchanges of gunfire lasting several hours, followed by explosions.
Afghan President Ashraf Ghani condemned the "terrorist" attack that "martyred and wounded the innocent" - students attending class - and ordered an investigation into the attack.
Both male and female students were studying at the center, preparing for entrance exams.
The UN Security Council also issued a statement condemning the "heinous and cowardly" attack.
"Children are not, and must never be the target of violence", said UNICEF's executive director Henrietta Fore.
The latest incident comes at a time of high tension following a series of attacks including a full-scale assault on the city of Ghazni last week. The Taliban has not taken any responsibility of the blast as of yet. Afghan special forces had arrived at the scene, Rahimi added. He said reinforcements have been dispatched to help recapture the checkpoints.
"A Taliban spokesman, Zabiullah Mujahid, said the group targeted a military base and two checkposts in Baghlan, killing 70 Afghan security forces, and seizing armoured vehicles and ammunition". "They are killing our educated people and every day they are killing us". Confusion about the death toll arose Wednesday as Kabul hospitals and government officials struggled to cope with the carnage.
Hundreds of people have fled the fighting in Ghazni, which has also killed about 100 members of the Afghan security forces.
Afghan forces appear to have finally pushed Taliban fighters from the strategic provincial capital.
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.
"They were facing severe shortages of food and drinking water as the power supply was also suspended two days ago", a Taliban commander, who declined to be identified, said by telephone.
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