The cause of the accident is under investigation but officials believe a tire may have blown out and caused the bus to veer off the bridge before dawn, said the emergency chief for the province of Salta, Francisco Marinaro yesterday.
It fell 15 meters and landed upside down, with the passenger cabin crushed almost flat.
Aerial photos showed the mangled vehicle lying in the riverbed, trailing a long strip of guard rail it ripped from the bridge on its way down.
The bus was part of a caravan of three carrying police to reinforce security in neighbouring Jujuy province, where a new governor is expected to announce job cuts soon.
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President Mauricio Macri sent his condolences to the officers' relatives and declared a day of national mourning.
"The Argentine people must stand with these families," he said.
Officials originally said 20 people were killed in the accident, but the death toll rose as emergency workers recovered bodies from inside the wreckage.
The accident occurred in a mountainous area with dense forests.
A local mayor, Gustavo Solis of Rosario de la Frontera, said the road where the accident took place is known to be in poor condition.