Eight cities in the region remain isolated and were running short of drinking water and fuel because of heavy flooding caused by the rains, officials said.
The region faces "the worst weather tragedy in history", Luiz Henrique da Silveira, the governor of Santa Catarina, told reporters on Tuesday.
Plea for aid
In the city of Blumenau, 500 troops were sent to aid rescue and recovery efforts after 13 people were killed by landslides and where drinking water was expected to be cut off until Friday.
"Mattresses, food, blankets - these are the main necessities we need to look after our displaced people," Joao Paulo Kleinubing, the town mayor, told the Reuters news agency.
"There is still a risk of landslides if it rains again so we are telling people in risky areas to leave their houses and seek shelter."
Luiz Inacio Lula da Silva, the Brazilian president, has offered federal help to the state, one of Brazil's wealthiest, and sent several ministers to the affected areas.
The civil defence agency said that 55,000 litres of drinking water had already been distributed but it appealed for more donations.
Rescue workers and army troops were forced to use helicopters and motor boats to reach stranded residents after the waters cut off crucial roads.
"Not even tractors can reach these areas because they sink, so access is only possible with aircraft," Major Marcio Alves, a co-ordinator with the civil defence agency, told Reuters.
The floods also shut down a pipeline carrying natural gas from Bolivia to Brazil on Monday, cutting off supplies to Santa Catarina and neighbouring Rio Grande do Sul state, the company that operates the line said.
The Latin American country is in spring season, when heavy rains in the southern part of the country are at their heaviest.