The storm had dumped more than 20 inches (50 cm) of rain in parts of central South Carolina since Friday, the National Weather Service said. The state climatologist forecast another 2 to 6 inches (5 to 15 cm) through Monday as the rain began to slacken.
South Carolina Governor Nikki Haley said parts of the state were hit with rainfall that would be expected to occur once in 1,000 years, with the Congaree River at its highest level since 1936.
"If you are in your house, stay in your house," Haley, holding a news conference, told state residents. "This is not something to be out taking pictures of."
Six weather-related deaths were reported in South Carolina, four of them from traffic accidents. Officials reported another two deaths in North Carolina.
Rains flooded highways along the South Carolina coast between Charleston and Georgetown, the weather service said. Georgetown, a city of 9,000 people, was mostly under water, and the four major highways leading into it were closed.
Flooding also hit the state capital, Columbia, where the Congaree rose 10 feet (3 m) in 12 hours, according to local officials. Residents were advised on the city's website to boil drinking water because of water line breaks.
State emergency officials urged residents not to travel due to unsafe roads, and curfews were imposed in eight cities or counties, including Columbia. Schools and universities canceled Monday classes.
A 70-mile (112-km) stretch of Interstate 95, a major East Coast highway, was closed because of high water.
Precipitation records fell in many places. Charleston broke its record for the greatest monthly rainfall for October in less than four days.
Amtrak, the passenger rail service, canceled its Virginia-to-Florida auto train and a passenger train from New York to Miami due to the flooding.