The blast in suburban Kabul, near a military base, happened at 1 am this morning, killing 15 people and wounding 240.
It was one of the largest ever in Kabul in terms of scale, flattening a city block and leaving a 30-foot crater in the ground. The blast was heard across the city of 4.5 million.
The president's office said 47 women and 33 children were among the casualties. The president's deputy spokesman Zafar Hashemi said about 40 of the wounded would remain hospitalised.
The Afghan intelligence agency announced more than a week ago that Mullah Mohammad Omar, the reclusive one-eyed founder and leader of the Taliban, had been dead for more than two years.
This sparked a leadership struggle among senior Taliban figures, raising concerns of a succession crisis that could splinter the group.
The implications of the Kabul attack undermine claims by security services and the government that the capital is immune from devastating attacks.
The Taliban said it was not behind the explosion, though it does not usually claim responsibility for attacks that kill or maim large numbers of civilians, especially women and children.
Ghani, freshly returned from medical treatment in Germany, visited the wounded in hospital as social media carried calls for blood donations.
