The deluges have displaced approximately 1,400 people in more than 100 municipalities across the state, the majority of whom civil defense officials said had been moved to shelters.
"We continue to work hard to locate the missing and to ensure the safety of at-risk areas," Governor Eduardo Leite said on social media Wednesday.
"Unfortunately, there is more rain forecasted for today."
Persistent rains have left some communities totally cut off thanks to destroyed bridges and blocked roads, while access to at least 20 areas along state highways has been restricted due to risk of further collapse.
Since Tuesday, rescuers have scrambled to free families trapped in their homes, many stuck on the roof as the waters rose, though ongoing bad weather has hampered the search efforts. Five people were reported dead Tuesday and 18 missing.
According to Leite, emergency workers were prioritizing responses to the most life-threatening situations.
In an effort to reach dry ground, residents of the small city of Encantado tried to leave the area on foot or by motorcycle over damaged and mud-caked roads, AFPTV images showed.
President Luiz Inacio Lula da Silva posted on social media that he had spoken with Leite and offered assistance.
"The federal government will join the efforts of state government and municipalities to get through this difficult time, which is the result of climate change affecting the planet," the president wrote on X, formerly Twitter, on Tuesday.
Around 130,000 people across Rio Grande do Sul were without drinking water, with telephone and internet service down in at least 60 municipalities as the rain continued.
The region's rivers are already swollen from previous storms, and torrential rains in late March in southeastern Brazil left at least 25 people dead in the states of Rio de Janeiro and Espirito Santo.
Brazil's south and southeast have been battered by a cold front that followed a wave of extreme heat.
