At least 20 other passengers were injured when the bus left the Pan-American highway and tumbled 80 meters (260 feet) down a jagged slope in the southern region of Arequipa.
"So far the bus accident has left 35 dead and 20 injured," the Interior Ministry announced on Twitter, quoting Arequipa police chief General Walter Ortiz.
Ortiz "specified that 45 people were registered as passengers on the bus. However, this does not match the number of people killed and injured," the ministry said.
State news agency Andina had earlier reported at least 20 people dead and 20 injured in the crash.The accident happened around 1.30 am (0630 GMT).
Rescue teams "have been working since dawn, coordinating the transfer and care of the injured," Arequipa governor Yamila Osorio wrote on her Twitter account.
The injured were taken to hospital in the city of Camana. Three seriously injured passengers were to be transferred by helicopter to regional capital Arequipa, Civil Defence chief Jacqueline Choque said.
The bus, operated by the Rey Latino company, had left the coastal town of Chala for Arequipa about four hours before the accident.
It was the second major accident on Peru's roads this year. On January 2, a bus crashed into a ravine in the country's central coastal area, leaving 52 dead.
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