Floods and landslides first hit Central Sulawesi province on Sunday and have left 22 dead and 47 missing, presumed buried under landslides, said Rustam Pakaya, who heads the health ministry's crisis centre in Jakarta.
Rising waters have now also hit North and South Sulawesi provinces, he said, leaving a total of 13 dead.
Some 45,000 people are estimated to be affected in Central and North Sulawesi but no figure was yet available for the southern province, he said.
A navy ship carrying a medical team was headed for Baturube, a coastal village nearest to the areas hit in Central Sulawesi, he said, while teams from Makassar in South Sulawesi were also dispatched to help survivors.
The police chief in worst-hit Morowali district in Central Sulawesi said 20,000 people have registered as fleeing their homes.
Suhartono said that relief aid from Jakarta including medicine, blankets, tents and body bags, had arrived on board a Hercules aircraft in the provincial capital Palu and was being distributed by truck, helicopters and a navy boat.
The Hercules left Jakarta on Tuesday, but was hit by engine trouble then poor weather.
A reporter for ElShinta radio, speaking from Uweruru, one of the villages worst hit by landslides in Central Sulawesi, said search and rescue efforts were continuing without heavy machinery amid heavy rains.
Indonesia has been repeatedly afflicted by deadly floods in recent years, with activists warning that logging and a failure to reforest denuded land in the world's fourth most populous country will continue to cause tragedies.