Bodies littered the scene and a towering plume of smoke rose from the area, which houses foreign embassies, after the blast blew out the windows in a number of missions and residences hundreds of metres (yards) from the epicentre.
Witnesses described dozens of cars choking the roads as wounded survivors and panicked schoolgirls sought safety, with men and woman struggling to get through security checkpoints to search for loved ones.
More than an hour after the explosion ambulances were still taking the wounded to hospital, as firefighters struggled to control blazes in several buildings.
Health ministry spokesman Ismael Kawoosi said around 90 people had been wounded in the blast, as well as the nine killed, but he cautioned the toll could rise.
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"They are still bringing bodies and wounded people to hospitals," he told AFP.
The Islamic State group has also claimed responsibility for several recent bombings in the Afghan capital, including a powerful blast targeting an armoured NATO convoy that killed at least eight people and wounded 28 on May 3.
Najib Danish, an interior ministry spokesman, said initial findings showed it had been a truck bomb.
Manpreet Vohra, India's envoy to Afghanistan, told the Times Now television channel the blast hit around 100 metres as the crow flies from India's embassy, one of several in the area.
Indian Prime Minister Narendra Modi tweeted: "We strongly condemn the terrorist blast in Kabul. Our thoughts are with the families of the deceased & prayers with the injured."
The explosion also shattered windows at the Japanese embassy. "Two Japanese embassy staffers were mildly injured, suffering cuts", a foreign ministry official in Tokyo told AFP.
Pentagon chief Jim Mattis has warned of "another tough year" for both foreign troops and local forces in Afghanistan.
US troops in Afghanistan number about 8,400 today, and there are another 5,000 from NATO allies, who also mainly serve in an advisory capacity -- a far cry from the US presence of more than 100,000 six years ago.
The blast was the latest in a long line of attacks in Kabul. The province surrounding the capital had the highest number of casualties in the first three months of 2017 thanks to multiple attacks in the city, with civilians bearing the brunt of the violence.
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