The attack rocked the center in the basement of a building in the west of the city at around 10:30 a.m. (12.30 a.m ET) Thursday morning. It also hit the Afghan News Agency, which has an office on the floor above, Afghan Interior Ministry spokesman Nasrat Rahimi said. Two more blasts followed at the same building, but caused no injuries.
The ISIS-affiliated Amaq News Agency said the terror group carried out the attack.
People carry an injured man to hospital after the suicide attack in Kabul on Thursday.
A crowd of just under 100 people were meeting at the cultural center to mark the anniversary of the Soviet invasion of Afghanistan when a bomber infiltrated the crowd and detonated the device, according to journalist Ehsanullah Amiri, who was at the scene.
Ambulances and police vehicles ferried the dead and wounded to nearby hospitals, Amiri said, as security forces cordoned off the site and blocked the main road approaching the scene. Authorities also warned onlookers to stay away from the site of the explosion, where there is also a Shia mosque.
Security personnel arrive at the site of the attack on Thursday.
Both the Afghan capital and the wider country are beset with attacks on its military, police and civilian populations. ISIS and the Taliban have both carried out several attacks in the country this year, and they have also been fighting each other over territory, particularly in the east of the country. The Taliban earlier denied responsibility for the blasts.
Earlier this week at least 10 people were killed after a suicide attacker detonated a bomb in an attack claimed by ISIS.
That attack targeted an office of the National Directorate of Security, Rahimi said, near the US Embassy and other diplomatic missions.
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