While the threat of flash flooding moved into Texas and the US Midwest, more than 11,000 Louisianans had signed up for disaster assistance, Louisiana's governor said on social media.
Over the weekend, floods inundated their homes, rising to rooftops in some areas and trapping people inside cars on a major interstate around Baton Rouge.
Emergency crews had rescued more than 20,000 people and continued to search for more after a storm dumped than 60cm of rain in three days in some places.
"Our state is currently experiencing a historic flooding event that is breaking every record," Louisiana Governor John Bel Edwards said in a statement on Monday, adding that he did not know when the water would clear. Some downstream communities were still experiencing cresting rivers.
"The water started rising three or four days ago and it's still coming up right now," said Lonnie Wells, 59, as he stood on flooded state highway in French Settlement, a town in southern Livingston Parish.
The Louisiana flooding, which prompted US President Barack Obama to issue a disaster declaration, resulted in seven deaths, National Weather Service meteorologist Jennifer McNatt said. Four occurred when high waters overcame motorists.
US rough rice futures surged the most in five years as floodwaters hit mature fields in the region, with farmers and millers bracing for crop loss.
Heavy rains also have slowed unloading of grain barges and loading of export-bound bulk cargo ships at grain terminals along the Mississippi River, causing a glut of supply that has weighed on corn prices.
The U.S. Coast Guard on Monday closed a section of the Intracoastal Waterway near Port Allen, Louisiana, due to flooding, but the Mississippi remained open to commercial navigation with no restrictions, a Coast Guard spokeswoman said.
The floodwaters were expected to linger.
"It is going to take a while for that water to make its way out," said the National Weather Service's McNatt, who is based in Fort Worth, Texas.
Rivers in Louisiana crested at record levels in multiple places, with the Amite River reaching 14 metres in Denham Springs, 1.5 metres higher than a 1983 record, McNatt said.
In flood-ravaged Livingston Parish, scores of people woke up on Monday in packed emergency shelters.
Pierre and Barbara Pitard, both 76, said they had just minutes to leave their home in Denham Springs as the water rose rapidly. They were finally rescued by boat and carried to safety on Saturday night, the vessel rocking as it hit submerged pickup trucks on streets inundated by water.
"It's already under water," Pitard said of his house. "I'm worried about how you go about getting it fixed because you've got thousands of people now with the exact same problems."
Localised flooding in Texas was a concern on Monday, the National Weather Service said, especially from Houston to the Hill Country region in the central part of the state. Rain also could bring flooding to Midwestern states including Missouri, Illinois, Indiana and Michigan, forecasters said.
