The Taliban-claimed assault -- the second carried out by the militant group in the Afghan capital in a week -- triggered chaotic scenes as terrified survivors fled the area scattered with body parts, blood and debris, and hospitals were overwhelmed by the large number of wounded.
It came as both the insurgents and the Islamic State group have escalated their attacks on Kabul, one of the deadliest places in Afghanistan for civilians.
Health ministry spokesman Waheed Majroh told AFP that the toll "now stands at 95 dead, 158 wounded", shortly after the interior ministry warned that an earlier death toll of 63 could rise.
The blast happened in an area where several high-profile organisations, including the European Union, have offices. Members of the EU delegation in Kabul were in their "safe room" and there were no casualties, an official told AFP.
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The suicide bomber passed through at least one checkpoint in the ambulance, saying he was taking a patient to Jamuriate hospital, an interior ministry spokesman told AFP.
"At the second checkpoint he was recognised and blew his explosive-laden car," Nasrat Rahimi said.
Rahimi told a news conference that most of the victims were civilians. He said the Taliban-affiliated Haqqani Network was responsible and four suspects had been arrested.
Twenty minutes before the blast an AFP reporter saw police checking ambulances several hundred metres from the scene of the explosion, as the drivers and patients stood on the street. Ambulances are rarely checked in the city.
The Taliban used social media to claim responsibility for the attack, which comes exactly a week after its insurgents stormed Kabul's landmark Intercontinental hotel, killing at least 25 people, the majority foreigners.
Photos shared on social media purportedly of the blast -- the deadliest in Kabul since a truck bomb ripped through the city's diplomatic quarter on May 31, killing 150 people and wounding hundreds -- showed a huge plume of smoke rising into the sky.
The Italian NGO Emergency said 131 wounded had been taken to its hospital, with its coordinator Dejan Panic tweeting that it had been a "massacre".
A photo posted on Emergency's Twitter account showed hospital staff treating injured people in an outdoor walkway next to a garden.
A man told Ariana TV he had taken his wounded brother to Jamuriate and Emergency hospitals but had been turned away.
Aminullah, whose stationery shop is just metres from where the explosion happened, said the force of the explosion shook the foundations of his building.
"The building shook. All our windows broke. The people are in shock in our market," he told AFP.
A man told Tolo News he was passing the area when the explosion happened.
"I heard a big bang and I fainted," he said, outside the Emergency hospital.
"There were dozens of people who were killed and wounded. There were pools of blood."
The offices of the High Peace Council, charged with negotiating with the Taliban which has been waging a more than 16-year insurgency in the war-torn country, are also near the blast site.
"It targeted our checkpoint. It was really huge -- all our windows are broken," Hassina Safi, a member of High Peace Council, told AFP.
"So far we don't have any reports if any of our members are wounded or killed."