"The storm has never been more risky than it is now", North Carolina's Republican Gov. Roy Cooper said during a press conference on Sunday.
The coastal city of Wilmington became an island amid heavy floods following the storm.
Mr Cooper added: "Catastrophic flooding and tornados are still claiming lives and property". More rain and flooding is expected in the days to come, as the now-tropical depression slowly heads towards the Ohio Valley.
The law mandates that businesses in the state aren't allowed to spike prices during any natural disaster for necessary items like food, water and hotel rooms.
An initial estimate from Moody's Analytics placed the cost of Hurricane Florence between $17billion (£13billion) and $22bn (£17 billion).
America's Cajun Navy, Louisiana Cajun Navy and the United Cajun Navy are on location to aid those in the rising flood waters.
In Wilmington, with its population of about 120,000, some 400 people have had to be rescued from flood waters, and most of the city remains without power.
North Carolina emergency response officials tweeted that 23 truckloads of military meals and bottled water were delivered overnight to Wilmington, the state's eighth-largest city.
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Police said that the five were arrested on Saturday, suspected of breaking into a local shop. It is where the popular series One Tree Hill was filmed.
In Anson County, east of Charlotte, a train derailed on Sunday evening, but it wasn't clear whether it was storm-related or if anyone was injured.
Rain from Florence, the storm system that was a Tropical Depression as of early Sunday afternoon, was starting to fall in parts of southern West Virginia at the close of the weekend ahead of what was expected to be a wet Monday statewide.
Some parts of the Carolinas have seen up to 40in (100cm) of rain since Thursday.
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"North Carolinians are resilient and we will come back from this. We don't want that at this time", Gov. Roy Cooper said during his noon briefing Monday. "But they will. And the question is how high will the water be, and we do not know".
"Three days of relentless rain from #Florence has resulted in significant flooding in #NC #SC", said Duke Energy, a major power supplier.
It had picked up pace somewhat, moving west at 8 miles per hour (13 kph), and its center was expected to move across the western Carolinas during Sunday and the Ohio Valley and Northeast United States on Monday and Tuesday.
The storm killed at least 11 people in North Carolina, including a mother and child hit by a falling tree, state officials said. The woman had driven around barricades to reach a closed road, the sheriff's office in Union County, near North Carolina's border with SC, said on Facebook. "I don't think we would leave it. Get the water out, start over", she said. In his path lay almost 2,000 factory farm cesspools loaded with hundreds of millions of gallons of toxic fecal waste, wastewater treatment plants, factories and communities, many of which were in the flood plain. A woman died in SC when her vehicle hit a fallen tree.
Cottonmouths, also known as water moccasins, are found in the eastern half of North Carolina.
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