Gunmen attacked the Communications Ministry shortly before midday in the center of the Afghan capital on April 20, officials told RFE/RL.
No other group claimed immediate responsibility, but the Afghan branch of the Islamic State group has previously carried out multiple deadly attacks in the capital.
An employee of the Telecommunication Ministry who was rescued, Hamid Popalzai, said "an explosion happened and then we heard the sound of gunfire and more explosions".
A suicide bomb was detonated at the entrance to the multi-story building housing the communications ministry in a busy commercial area of the city.
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Parliamentary member Harsha de Silva said foreigners were among the dead or injured, but did not provide further details. The Archbishop of Colombo is calling for those responsible for the Easter Sunday blasts to be punished "mercilessly".
In a statement, the interior ministry said four civilians and three soldiers had been killed, though unverified social media posts suggested the final toll could be higher.
The attack marked a return to the kind of complex urban attack that have been familiar features of the Afghan conflict over recent years.
Sources said security forces and ambulances have arrived at the attack scene near the Ministry of Communication and Information Technology and all ways connected to the area have been cordoned off by security forces.
Wahidullah Mayar, spokesman for the Public Health Ministry, said the wounded people were evacuated to hospitals, three of them women.
Afghan president Ashraf Ghani strongly condemned the attack in a statement, saying the enemies of Afghanistan, by targeting civil servants, are trying to create terror among the people.
"Operations finished. All suicide bombers killed & more than 2000 civilians staff rescued", the Minstry of Interior said on Twitter.
Local television footage showed a small plume of smoke near the ministry, and people climbing out the windows on a lower level.
Eleven people died in an explosion and the ensuing gunfight at Afghanistan's Ministry of Communication and Information Technology in Kabul on Saturday.
Un nouveau-né vivant retrouvé dans un sac poubelle — Aube
Je lui ai dit de déchirer le sac et elle m'a confirmé, paniquée, que c'était un bébé. L'alerte a été donnée par des riverains, précise encore le journal local.
The explosion comes the week after the Taliban announced their annual spring offensive and amid ongoing fighting across Afghanistan.