The "risk to life is rising" from Storm Florence, North Carolina's governor, Roy Cooper, has warned.
In a briefing for the media, he said people should stay off the roads as the threat from floods continued to spread.
Despite weakening since hitting the coast on Friday, Storm Florence has been dumping "epic" rain as it moves through North and South Carolina.
At least 15 people have died in storm-related incidents, 10 in North Carolina and five in South Carolina.
The slow-moving storm is heading west but is due to turn north towards Ohio.
What are the warnings?
Florence, which started out as a hurricane, has now weakened to a depression, the National Hurricane Center (NHC) said on Sunday, but flash flooding and river floods will continue over a significant portion of the Carolinas.
Winds had sustained speeds of 35mph (55km/h) with faster gusts, the NHC said.
In his latest update on the situation in North Carolina, Mr Cooper said the storm had "never been more dangerous than it is now".
Rivers were still rising and would not crest until later on Sunday or Monday. Nearly two feet (60cm) of rain had fallen in many places.
The governor also warned of landslides once the weather system reached more mountainous areas.
More than 900 people have been rescued from flooded areas in the state.
Authorities in the North Carolina city of Fayetteville ordered residents living near two rivers to evacuate.
"If you are refusing to leave during this mandatory evacuation, you need to do things like notify your legal next of kin because the loss of life is very, very possible," Mayor Mitch Colvin said.
US President Donald Trump has declared a disaster in eight counties in North Carolina - a move that will help free up federal funding for recovery efforts. The state is asking for more counties to be added to the list.
What do we know of the victims?
Among the dead are a mother and her seven-month baby, who were were killed when a tree fell on their home in Wilmington, North Carolina on Friday.
A 71-year-old man died when he was blown down by high winds while checking on his dogs, while in South Carolina two died from carbon monoxide poisoning caused by a generator inside their home and two men died in separate road accidents.
What has the damage been?
Florence first landed in North Carolina as a category one hurricane.
The storm has lost strength as it moves inland but it has knocked out power for 800,000 businesses and homes in the Carolinas. Many are still without power.
Fifteen thousand people are being housed in temporary shelters in North Carolina.
Ten mass-feeding kitchens are being set up.
The coast guard and volunteer boats have been helping people left stricken by rising flood waters.
Scores of residents had to be rescued from flooding by emergency responders and volunteers in New Bern, North Carolina, on Saturday.
A local, Charles Rucker, told AFP news agency: "It was like a bullet train coming through the living room. Nothing I ever experienced before, I was truly scared."
Police in Wilmington, North Carolina, said they arrested five people for allegedly looting a discount store.