The attack took place at about 10.30am local time. "We still do not know the target of the attack, but Afghan Voice Agency is in the area of the attack", interior ministry spokesman Najib Danish said.
Wahid Majroh, spokesperson for the Afghan ministry of public health, said 41 people had died.
The center is located in the Shiite-dominated Dasht-e-Barchi neighborhood in the west of the capital.
Police spokesman Basir Mojahid told NBC News that at least 25 people had been killed and 32 others injured.
Aamaq in its statement also claimed the center was funded by Iran and propagating Shiite beliefs.
Afghan president Ashraf Ghani called the attack a "crime against humanity".
On Monday, eight people were killed and two injured in a suicide bomb attack near an office of the National Directorate of Security (NDS) in the capital city's Shashdarken neighbourhood.
Mr Johnson said: "I am appalled by this despicable attack on a cultural centre in Kabul which has claimed so many innocent lives, and my heartfelt condolences go out to the victims and their families". A neighboring news agency, Afghan Voice, was also hit, prompting fears about the safety of media organizations and journalists in the country ravaged by militants.
Rahimi said the main blast was followed by two smaller bomb explosions that did not cause casualties. They then set off explosive devices in the basement of the building where scores of people had gathered to mark the December 1979 invasion of Afghanistan by the former Soviet Union, he said.
No one immediately claimed responsibility for the attack but the local Islamic State affiliate has carried out several attacks targeting Shiites in Afghanistan.
An Afghan official says a roadside mine has exploded, killing six children in northern Balkh province. Kabul has become one of the deadliest places in war-torn Afghanistan for civilians in recent months, as the Taliban step up their attacks and the Islamic State group (IS) seeks to expand its presence in the country.
F1 sees distinguished manufacturers make a welcome return
It would also be nice to see a more competitive side to the sport, which usually sees one side dominate the entire season. The team is looking at Charles Leclerc from Ferrari, Marcus Ericsson or Antonio Giovinazzi who is a reserve for Ferrari.
Samsung shares hurt by negative Morgan Stanley forecast
The company will be starting construction soon on a special EUV facility as part of their Hwaseong complex in South Korea. The Note 8 has seen an incredible return to form for the company and saw over 4 million devices sold around the world.
Total integration of fitness apps may be the next step.
An example of a simple, natural replacement item in this instance is the Under Armour Gemini 3 RE smart shoes. Not their departure, by any means, but the total integration of their smart features into our everyday items.
What Are Online Games
If we are all honest with each other, there is no denying that when real money is involved the activity is no longer for leisure. And in some cases, it is even used to refer to something that is done elsewhere for an income but now being done for recreation.