The bus was travelling in a convoy of three coaches each carrying about 60 police officers – all in their late teens and early 20s – when the driver lost control as it was crossing the bridge at about 2am local time (5am GMT).
Television images showed the overturned bus and rescue crews at the scene working to free trapped passengers in a mountainous area of the northern province of Salta, a city about 932 miles (1,500km) north of capital, Buenos Aires.
Officials said survivors were being taken to a nearby hospital. Ten were receiving treatment and four were said to be in a serious condition.
“The bus lost control while entering the bridge and fell into the creek bed below,” said a statement issued by the National Gendarmerie, the special force usually charged with patrolling frontier regions.
They were heading to the province of Jujuy, Argentina’s most northerly region, which borders Bolivia, in response to local protests. Roads in Argentina, a large country with a land mass about four times the size of the US state of Texas, are poorly maintained in rural areas.
Angel Marinaro, civil defence director for the province, confirmed in a radio interview that the driver of the bus seemed to have lost control of his vehicle on the bridge.
Provincial emergency directory Ernesto Flores told local radio station La Red: “We are talking about close to 30 dead. Between 50 and 60 border patrol officers were on board. Some are still trapped.”
Gustavo Solis, mayor of Rosario de la Frontera in the province, told one newspaper that the road where the accident happened is known to be in poor condition, earning it the local nickname, the “death road”: “Those of us who know the area try to avoid driving at night.”
The government announced that security minister Patricia Bullrich and National Gendarmerie director Omar Ariel Kannemann were travelling to the scene.
President Mauricio Macri, elected last month on a platform that included improving Argentina’s rural roads, sent his condolences to families of the victims of the crash.
“We need to improve our highways so these things don’t keep happening,” Mr Macri told reporters at a news conference in Buenos Aires province.
Border security has become a hot issue in Argentina as the country has emerged as part of a route used for smuggling Andean cocaine to Europe and for human traffickers sending Syrian refugees to the West.
Last year 18 people were killed in Argentina when a bus crashed into a lorry driving on the wrong side of the motorway.
The truck, which had a Brazilian licence plate, was stolen and was being driven at high speed.
An investigation into the latest crash was launched yesterday as the search for survivors continued.