"We are praying for the missing to be found alive. But we are very worried because bodies are starting to turn up on beaches and on riverbanks," Teotonio Vilela Filho, the state governor, said.
The torrents swept away more than 40,000 houses, entire bridges and streets, as well as rail lines in 22 towns across Alagoas, Vilela said.
Twenty-six people have been confirmed dead in Alagoas and 13 in Pernambuco state.
Power and phone services have been cut off in many areas and officials fear there could be many deaths unreported.
Mudslides have hit areas where shacks were built on hillsides.
Some regions reported over 36 centimetres of rainfall over the past three days.
In May 2009, flooding in the same area killed at least 44 people and displaced 380,000 others.