"Thirteen people have died and the toll hasn't risen" since the accident, police spokesman Khulekani Mamba told AFP.
Local media gave the same death toll, yet pro-democracy activists from the Johannesburg-based Swaziland Solidarity Network today said 65 were killed.
Eleven of the victims were girls from the village of Phonjwane in eastern Swaziland, according to the daily Times of Swaziland.
The crash happened Friday night when their open truck smashed into a car on the road between the tiny kingdom's two main cities, Mbabane and Manzini, en route to the traditional Reed Dance, activists said.
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Tens of thousands of young virgins dance before the polygamist king, who can select one of them as a new wife.
Swaziland Solidarity Network (SSN) activists claimed the ruler had fabricated the lower death figure.
"It's lies. This puts the king in an embarrassing situation and he is trying to undermine the toll," SSN spokesman Lucky Lukhele told AFP.
Mswati, Africa's last absolute monarch, chose his 14th wife at the celebration in 2013. He has ruled Swaziland since his father's death in 1982.