The head of Peru's Civil Defense Institute, Alfredo Murgueytio, told the daily El Comercio in an interview posted online that rescuers pulled 11 bodies from the rubble, and that 10 people are still missing.
Mayor Garcia said that some of the missing people may have fled into the hills to save their lives.
"Whole families are missing," said Garcia. More than 80 families live in the village, he said.
El Porvenir residents are mostly coffee farmers, officials said.
Heavy rain in Peru's Andean region in recent weeks has triggered several landslides.