Two children were among the dead and 84 people were injured in the blast, according to a Health Ministry spokesman.
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.
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.
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.
Afghan President Ashraf Ghani condemned the attack, saying that the government was determined to eliminate terrorist groups.
"Terrorists always hide their defeat against our security forces by attacking mosques, religious places, and educational institutions, and killing our people, including women and children," Ghani wrote on Facebook.
"Terrorist groups and their supporters should understand that by doing such crimes they cannot gain success. Day by day, our peoples' hate increases as everyone recognizes them."
US Ambassador to Afghanistan John R. Bass said: "The United States continues to stand with all Afghans in their pursuit of peace, security, and prosperity."
"This incident once again demonstrates the depravity of those who seek to undermine peace and stability in Afghanistan," he said. "We remain confident the Afghan government and people, supported by their friends and partners, will defeat those behind these terrible acts."
The United States has supported the Afghan government in its fight against ISIS, but has dramatically decreased the number of its troops this year.
Human rights organization Amnesty International said the attack underscored the dangers faced by Afghan civilians and blasted European leaders for forcibly returning Afghan asylum-seekers to the country.
"With the Afghan capital hit once again, no one can credibly claim that Kabul safe. The European governments who insist on this dangerous fiction by forcibly returning Afghans are putting their lives in danger," Amnesty International South Asia Director Biraj Patnaik said.
Patnaik added that it was one of the deadliest years on record in the country.
Attacks rock Kabul
A number of other attacks have targeted the city in recent months:
Dozens of Afghans were killed in two mosque attacks
, claimed by ISIS.
A suicide bombing near a military academy took another 15 lives
, claimed by the Taliban.
At least 41 soldiers were killed
in an attack on their base in eastern Afghanistan, claimed by the Taliban.
A suicide bomber killed three people
in a blast outside a cricket stadium in Kabul.
20 people killed in an attack on a Shiite mosque, for which ISIS claims responsibility.