Florence continues to pour rain on North Carolina and the authorities warn residents "the worst is yet to come", as the rivers inland are likely to be flooded.
The death toll rose to at least 14 from Florence, which crashed into the state as a hurricane on Friday, bringing record rainfall.
It had weakened to a tropical depression on Sunday, but it was forecast that it would shed 13 to 25 centimeters of rain in North Carolina, bringing the total rainfall in some areas of the interior to 40 to 50 cm and more than 76 cm closer to the coast, according to the National Hurricane Center. .
More than 900 people were rescued from the increase in floods and 15,000 remained in shelters in the state, Cooper said at a press conference on Sunday.
The people who evacuated were anxious to return to their homes, but the authorities urged them to stay away.
"Our roads are flooded, there is no access to Wilmington," New Hanover County Commission President Woody White said at a news conference. "We love you at home but you can not come yet."
The fresh evacuations were ordered further inland as the rivers reached the ridge and spilled out from their margins.
In Fayetteville, a city in North Carolina with some 210,000 people 145km from the ocean, authorities told thousands of residents near the Cape Fear River and Little River to leave their homes on Sunday afternoon because of the risk of flooding.
"The worst is yet to come," Mayor Mitch Colvin told a news conference on Saturday.
North Carolina Director of Emergency Management Michael Sprayberry said it was too early to calculate how many people in the state would be left homeless by the storm.
"At this moment, we think there will be tens of thousands of homes that will be damaged," he said.
About 756,000 homes and businesses were without power in North Carolina, South Carolina and neighboring states, down from a maximum of nearly one million.
Florence set a state record for hurricane rainfall, shedding 86cm in Swansboro, North Carolina.
North Carolina officials warned motorists not to drive on roads in a large area due to dangerous conditions in the southeastern part of the state. The swelling of rivers and streams threatened dams and bridges.
The flood could stain the waterways with dark charcoal ash. But so far officials said the state's numerous toxic waste lagoons had withstood the storm.
The White House said President Donald Trump approved the availability of federal funds in some affected counties. Trump, who plans to visit the region this week, tweeted his condolences to the families and friends of those who died.