Santoso Ginting, the district police chief, said on MetroTV: "Of 73 people reported [missing], we have recovered 40 bodies. Four people were found alive and we are still searching for 29 more people."
Indonesia is in the middle of the rainy season when landslides are frequent in the country.
Tropical downpours can quickly soak hillsides where deforestation has left little vegetation to hold the soil.
Quake hits homes
Indonesia is a vast chain of 17,000 islands where millions of people live in mountainous areas or near fertile flood plains.
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A moderate earthquake measuring 5.3 on the Richter scale also struck Indonesia's Papua island on Saturday, damaging homes, but caused no serious damage or deaths, a meteorological official said.
The quake struck 67km southeast of Manokwari, the capital of West Irian Jaya province, at a depth of 33km, an analyst at the meteorology and geophysics agency, said.
Indonesia lies in the so called "Pacific Ring of Fire" where seismic activity is frequent because of the shifting of tectonic plates.