SAO PAULO, Sep 6 (Reuters) - The death toll from heavy rains that devastated Brazil's Rio Grande do Sul state rose to 31 on Wednesday (Sep 6), local authorities said, as an extratropical cyclone batters the region, flooding homes and swelling rivers.

Video obtained by Reuters showed houses in the small town of Mucum submerged by rising water, while streets and rivers were flooded. Nearby cities such as Lajeado and Roca Sales have also been severely affected.

The floods in Rio Grande do Sul were the latest in a series of such disasters to have recently struck Brazil, where more than 50 people were killed in Sao Paulo state earlier this year after massive downpours caused landslides and flooding.

The colonial-era city of Petropolis near Rio de Janeiro and Bahia state also suffered similar disasters recently, as well as Santa Catarina, a state neighbouring Rio Grande do Sul where an additional victim was confirmed on Tuesday.

President Luiz Inacio Lula da Silva said on Wednesday he had spoken to Rio Grande do Sul Governor Eduardo Leite to offer the federal government's full support for the state to "face this crisis."

Lula sent two ministers to the state to oversee search and rescue efforts and said Vice President Geraldo Alckmin would also be "on standby" to travel there.

Weather forecaster Climatempo said that even though showers had stopped on Tuesday, they were expected to return to Rio Grande do Sul on Wednesday and Thursday before dissipating by Sunday, with the state still on alert for floods.

"A combination of lower air pressure and the accumulation of warm humid air will again generate heavy clouds over Rio Grande do Sul, which will cause more heavy rain," Climatempo said in a statement.

Rio Grande do Sul is home to some 10.9 million people and hosts several industries, in addition to being among the top grain-producing states in the country. It borders Uruguay and Argentina.