As flooding continues to inundate North Carolina, the death toll from Florence has risen to at least 32, with 25 deaths confirmed in North Carolina.
The state's governor, Roy Cooper, said on Monday that the "epic storm" was still an immediate danger as rivers reach major flood levels.
The coastal city of Wilmington became an island amid heavy floods following the storm.
Officials have warned evacuated residents to stay away.
At a news conference on Monday, Gov Cooper said "catastrophic flooding and tornados are still claiming lives and property" across the state.
"For many parts of North Carolina the danger is still immediate," he said. "Some areas have not seen the worst flooding yet. This is a monumental disaster for our state."
An initial estimate from Moody's Analytics puts the cost of Florence between $17bn (£13bn) and $22bn, making the storm one of the 10 costliest hurricanes in US history, according to NPR.
Most of the monetary damage is due to property loss, and the company said these figures could rise as inland flooding continues.
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.
The governor said that 23 truckloads of supplies were able to make it into Wilmington this morning, though officials are uncertain whether the single road into the city will remain functional as rivers continue to flood.
The National Weather Service has warned of at least two further days of possible flash flooding in the area before conditions are forecast to improve.
"Do not come here," New Hanover County Commission Chairman Woody White said. "We want you home, but you can't come yet."
A city-wide curfew has been extended after five people were arrested on suspicion of looting from a store on Saturday.
The area is usually best known as a filming location for US dramas One Tree Hill and Dawson's Creek, and as the childhood home of US basketball legend Michael Jordan.
What's the latest on the storm?
Florence has now weakened to a tropical depression with winds of 30mph (45km/h), according to the National Hurricane Centre.
Some parts of the Carolinas have seen up to 40in (100cm) of rain since Thursday.
On Monday, the National Weather Service announced that the Cape Fear River near Fayetteville, North Carolina, is expected to reach the major flood stage - levels over 60ft (18m) - by this evening.
The Cape Fear at #Fayetteville #NCwx continues to rise, and is expected to enter into the major flood this afternoon/evening. At this stage, numerous structures and roadways are flooded, and lives are put at risk. Follow all local evacuation orders. https://t.co/KbSBxyk7DR pic.twitter.com/PcsDexokXz— NWS Raleigh (@NWSRaleigh) September 17, 2018
There were several tornado warnings across North Carolina on Monday morning.
One twister touched down in Elm City, causing some damage to buildings and power lines, according to local media reports.
In Richmond, Virginia, one person died in a tornado on Monday afternoon as Florence began making its way north.
Officials in North Carolina say some 900 people have been rescued from floodwaters by the US Coast Guard and volunteers, and about 14,000 people are still in emergency shelters.
Awful. This is Hwy 145 north of Chesterfield. Bridge gave out. Sheriff says Truck driver is ok. pic.twitter.com/ijnzQCckuA— Greg Suskin (@GSuskinWSOC9) September 17, 2018
US President Donald Trump - who may visit North Carolina in the coming days - has declared a disaster in several North Carolina counties, freeing up federal funding for recovery efforts.
FEMA, First Responders and Law Enforcement are working really hard on hurricane Florence. As the storm begins to finally recede, they will kick into an even higher gear. Very Professional!— Donald J. Trump (@realDonaldTrump) September 16, 2018
Gov Cooper said he has been in touch with Department of Homeland Security (DHS) Secretary Kirstjen Nielsen, who visited North Carolina on Monday.
"We know that we're going to need significant federal resources, and they have promised them across the board," Gov Cooper said on Monday of Fema and DHS.
Power companies are working to restore power to the nearly half a million homes and businesses in both states that are still without electricity.
The storm has begun to move into Virginia and West Virginia, and is expected to turn toward New England on Tuesday.
What do we know of the victims?
On Monday, police in Union County, North Carolina, recovered the body of a one-year-old boy who had been swept away by floodwaters.
The boy's mother had driven around a barricade in the road and ended up stalled in rushing water. As she tried to leave the car, she lost grip of the boy and he was carried off in the floods, the News & Observer reported.
An 88-year-old man was also found dead in Union County on Monday, next to a car that had been submerged in the floods.
Among the other fatalities were two men in their 70s who died in Lenoir County - one had been connecting extension cords and another was blown by high winds when checking on his dogs.
Four road deaths in South Carolina have been blamed on the storm, and two people died from carbon monoxide poisoning caused by a generator inside their home.