In Virginia, near state capital Richmond, emergency services said one man died after a building collapsed during severe weather, though it was not clear if that death was directly linked to Florence.
More than a dozen rivers across North Carolina were at major flood stage on Monday or threatening to rise to critical levels.
“Many roads in our state are still at risk of floods,” Cooper said, warning people who have been evacuated not to return home yet and others not to go out if they do not need to.
“Please don’t make yourself someone who needs to be rescued,” he said.
Wilmington, on the banks of the Cape Fear River in North Carolina, was almost completely cut off by land but emergency management teams managed to truck food and water overnight into the port city of 120,000 people.
North Carolina emergency department officials said 23 truckloads of Meals, Ready to Eat — packaged US military rations — and crates of bottled water had been sent into Wilmington.
And a wave of solidarity rippled through hard-hit New Bern, where hundreds of people lined up as a local supermarket distributed fried chicken and hamburgers.
“This community, the most marginalized and economically deprived in town, has been hit the worst. They are still is without power,” said Braden Welsh, one of those behind the initiative.
“We wanted to pump their spirit up.”
Nearly three feet of rain
Local artist Kevin Bryant praised the effort, saying “it’s good to get some support.”
“I lost everything in the flooding,” he said. “We didn’t think it would be that bad. It happened so fast.”
The National Weather Service released rainfall totals as of 2:00 pm (1800 GMT) for parts of North Carolina. The largest amount so far was in Elizabethtown, which has received 35.93 inches (0.91 meters).
The most rainfall recorded in South Carolina was in the town of Loris, where 23.81 inches (0.6 meters) fell.