Many of the dead, including women and children, were burned beyond recognition and dozens of others were left wounded in the accident in Ghazni province, near the Afghan capital, one of the areas worst affected by the Taliban insurgency.
"The death toll has soared to 73, most of them severely burned," ministry spokesman Ismail Kawoosi told AFP, warning that the toll was expected to rise still further.
Kawoosi gave a sharply higher toll than other officials. Ghazni's governor Mohammad Aman Hamimi earlier reported seven fatalities but his own spokesman gave a death toll of 50.
Afghanistan has some of the world's most dangerous roads and deadly accidents are common.
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At least 18 people were killed in May last year when a minivan overturned in the western province of Badghis.
And in April 2013 a bus hit a wrecked fuel tanker in the southern province of Kandahar, killing 45 people.
The World Bank in November signed off a USD 250 million grant to upgrade roads crossing Afghanistan's Hindu Kush mountains, crucial trade links that are often closed in winter by snow.