Fazaludin Agha said it was not known who fired the rocket that set off the initial explosion, or from where. But Afghan officials in Pakistan say the explosion appears to have been an accident.
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"There were a series of deafening explosions which started shaking our houses," said Ahmed Ali Achkazai, a resident of the Pakistani border town of Chaman, a few kilometres from Spin Boldak.
He said he ran outside and saw balls of fire rising into the air over Spin Boldak.
Those wounded in the blasts were taken to hospitals in Chaman and the main southern Afghan city, Kandahar.
Afghan soldiers are reportedly digging through the rubble of buildings looking for survivors. The area, a residential district of the town, is said to be littered with unexploded ammunition and rockets.
Mr Agha said earlier the bodies of eight Afghan soldiers had been recovered.
Aid centre hit
A United Nations aid warehouse in Spin Boldak was among the buildings caught in the blasts, and one of the organisation's workers was slightly injured.
UN spokesman Khaled Mansour said the warehouse received food from Pakistan which was then distributed to 60,000 displaced people in southern Afghanistan.
"It seems most of the food is intact, but two huge storage tents and three containers used as offices were destroyed," he said.
The ammunition store was set up by the former Taleban regime in what was a religious school, in the centre of the town.
The BBC's Susannah Price, who is in the region, says there are many such depots across Afghanistan filled with weapons - a result of more than two decades of war in the country.
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