The accident occurred on Saturday in the province of Talara, on the Panamericana Norte motorway, between the districts of El Alto and Los Organos.
RPP said that unconfirmed reports indicated that the death toll from the accident stood at 25, although the number of fatalities has not been officially confirmed.
The bus, which belonged to Q'orianka Tours, departed Lima and was headed towards Tumbes, near the border with Ecuador.
The accident occurred in the early hours of Saturday, when the driver lost control of the bus while trying to navigate a sharp road curve and plunged down a gorge, RPP said.
The exact cause of the tragedy is under investigation.