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.
An AFP reporter saw "lots of dead and wounded" civilians in the Jamuriate hospital, which is metres away from the blast and where medical staff struggled to treat the bloodied men, women and children lying on the floor in corridors.
Health ministry spokesman Waheed Majroh said 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 said.
The force of the explosion shook windows of buildings at least two kilometres (more than a mile) away and caused some low-rise structures in the immediate vicinity to collapse.
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 said.
"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 International Committee of the Red Cross in Afghanistan condemned the use of an ambulance in the bombing, saying on Twitter it was "unacceptable and unjustifiable".
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.
Near the blast site civilians walked through debris-covered streets carrying wounded on their backs as others loaded several bodies at a time into ambulances and private cars to take them to medical facilities around the city.
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.
"They are asking people with non-life threatening wounds to go to other hospitals," he said.
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 said.
’Pools of blood’
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 attack was condemned by the presidential palace as a "crime against humanity". There was international outcry too, with NATO, the US embassy in Kabul and British foreign minister Boris Johnson among those expressing horror at the latest attack.
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, said.
"So far we don’t have any reports if any of our members are wounded or killed."
A security alert issued on Saturday morning had warned that the Islamic State group was planning "to conduct aggressive attacks" on supermarkets, shops and hotels frequented by foreigners.
Trump urges ’decisive action’
President Donald Trump called for "decisive action" against the Taliban on Saturday after Kabul bombing.
"I condemn the despicable car bombing attack in Kabul today that has left scores of innocent civilians dead and hundreds injured. This murderous attack renews our resolve and that of our Afghan partners," Trump said in a statement.
"Now, all countries should take decisive action against the Taliban and the terrorist infrastructure that supports them."
"The Taliban’s cruelty will not prevail," Trump added.
"The United States is committed to a secure Afghanistan that is free from terrorists who would target Americans, our allies and anyone who does not share their wicked ideology."
US Secretary of State Rex Tillerson condemned the "senseless" attack, insisting there can be "no tolerance for those who support or offer sanctuary to terrorist groups."
"The Taliban’s use of an ambulance as a weapon to target civilians represents inhumane disregard for the people of Afghanistan and all those working to bring peace to the country," Tillerson said, adding that the attack breached "the most basic international norms".
"All countries who support peace in Afghanistan have an obligation to take decisive action to stop the Taliban’s campaign of violence."
Eiffel Tower goes dark
The Eiffel Tower would cut its lights on Saturday night to commemorate those killed and wounded in a devastating ambulance bombing in Kabul, Paris Mayor Anne Hidalgo said on Twitter.
"Tonight at midnight the Eiffel Tower will go out in hommage to the victims of the horrific attack that struck Kabul," Hidalgo said.
"The city of Paris and Parisians are with the Afghan people who are once again facing terrorist barbarity."
A statement from France’s foreign ministry condemned Saturday’s attack and offered support for Afghanistan’s fight against "the scourge of terrorism".
The icon of Paris’ skyline is often dimmed or made to display the colours of a country’s flag in shows of respect for those killed or maimed by terror attacks.