Pounding rain has inundated southern Louisiana with "historic" flooding, killing at least six people as exhausted rescue workers saved more than 20,000 others from their swamped homes.

The latest casualty of the flooding was a 59-year-old man who was suddenly carried away by a powerful current while walking along a road in Tangipahoa City. Another man was swept away as he drove his truck down a highway. And a woman's body has been found in a submerged car near the Baton rouge airport.

More from IBTimes UK

The state's governor warned it is far from over. "The water's going to rise in many areas. It's no time to let the guard down," said Governor John Bel Edwards.

Edwards has declared a state of emergency, calling the massive floods "unprecedented" and "historic." He said thousands of homes have already been damaged.

"This is a major disaster," he said. "This is an ongoing event and we are still in the response mode."

President Obama has also declared a major disaster in the hard-hit parishes of East Baton Rouge, Livingston, St Helena and Tangipahoa, freeing up federal funding for flood-related assistance, NBC reported.

In one particularly dramatic flood rescue in Baton Rouge caught on video obtained by CNN, a woman had to be freed through a rip cut into the soft top of her car as her vehicle rapidly sank in a flooded creek.

"Please help me!" the woman pleaded. "We're coming! We're coming!" the rescuers shouted to her. Once she was freed, one of the men then dove again into the murky water to save her dog.

Though areas just now are experiencing drier weather, residents in affected areas were warned to stay at home and off the roads — unless they're told to evacuate.

"Even a typical afternoon summer thunderstorm has the potential to cause flooding," Edwards said.

The Amite River had already reached historic levels and was expected to rise 4.5 feet above the record high, according to The Weather Channel.

Livingston Parish was among the hardest hit, with some towns completely cut off. Hundreds of motorists were still stranded along the interstate.

More than 100 roads have been closed across the state. In Jefferson Davis Parish, so many roads are impassable that a 6pm curfew has been imposed so motorists do not get stranded overnight.

Tens of thousands of displaced people are holed up in state and locally run shelters, while others are bunking with relatives and friends who have homes on higher ground.

More than 1,700 rescue personnel have been mobilised, including members of the Coast Guard and the National Guard.

The Coast Guard was using helicopters to pluck people off the roofs of their flooded homes in exhausting, risky operations.