South Carolina schools were shut on Monday and several motorways were closed as rain continued to fall.
One weather station in Columbia – South Carolina’s capital – recorded 17 inches (43cm) in as many hours on Sunday.
The torrential rains have been made worse by a weather system connected to Hurricane Joaquin in the Caribbean.
The storm is not expected to hit the eastern US, but the moisture associated with it is contributing to heavy rainfall.
“The flooding is unprecedented and historical,” said Dr Marshall Shepherd, a meteorologist and director of the atmospheric sciences program at the University of Georgia.
Many of the victims have drowned after flood waters swept over their vehicles.
South Carolina Governor Nikki Haley urged residents to stay indoors.
“The water is not safe and a lot of areas across the state where you see this deep water, it’s got bacteria in it. So, stay inside and don’t get in there,” she said.
President Barack Obama has declared a state of emergency in South Carolina. The move means state and local authorities can receive federal help to deal with the flooding.
“We have every ambulance in the county out responding to calls. People are being moved from their homes in boats,” Georgetown County spokeswoman Jackie Broach told Reuters.
About 100 people were rescued from their cars on flooded roads on Saturday night.
In the historic city centre of Charleston, many streets have been closed and sandbags have been piled up to keep floodwaters out.