Bodies littered the scene and a towering plume of smoke rose from the area, which houses foreign embassies, after the blast in the morning rush hour blew out the windows of several missions and residences.
Witnesses described dozens of cars choking the roads as wounded survivors and panicked schoolgirls sought safety. Men and women struggled to get through security checkpoints to search for loved ones.
It was not immediately clear what the target was. But the attack underscores spiralling insecurity in Afghanistan, where a military beset by soaring casualties and desertions is struggling to beat back the insurgents. Over a third of the country is outside government control.
"Unfortunately the toll has reached 80 martyred (killed) and over 300 wounded, including many women and children," said health ministry spokesman Waheed Majroh, adding the figures would continue to climb as more bodies are pulled from the debris.
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The interior ministry, which put the number of wounded at 320, said a suicide bomber had detonated an explosives-packed vehicle in Zanbaq Square around 8:30 am. "More than 50 vehicles were either destroyed or damaged," it said in a statement.
The ministry called on Kabul residents to donate blood, saying hospitals were in "dire need".
The insurgent group rarely claims responsibility for attacks that kill large numbers of civilians.
The Islamic State group has 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.
Manpreet Vohra, India's envoy to Afghanistan, told the Times Now television channel the bomb went off around 100 metres 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.