"This system is unloading epic amounts of rainfall, in some places measured in feet and not inches", North Carolina Governor Roy Cooper told a news briefing about a storm that forecasters said was 480km wide.
Across the two states there are some 30,000 people staying in emergency shelters.
Other areas throughout the region reported flooded and impassable roads, downed trees and power lines and power outages of more than 125,000 customers.
"The fact that there haven't been more deaths and damage is incredible and a blessing", Rebekah Roth said yesterday while walking around Wilmington's Winoca Terrace neighborhood.
Florence slammed into the North Carolina coast as a large hurricane Friday, dumping almost three feet (1 meter) of rain and swelling the region's rivers.
At 11am yesterday, the hurricane centre said Florence had maximum sustained winds near 75kph and continued to produce catastrophic flooding in the Carolinas. On Friday afternoon, it was traveling at just 3 to 5 miles per hour, still near the coast.
He said the storm had killed at least five people, but there were fears that number could rise. That could affect the infrastructure, bridges, residences, farms and other buildings, Dahler said.
As many as seven deaths have been attributed to the storm so far. The page says service animals aren't barred from evacuation shelters, beaches shouldn't be used for sand bags, and evacuation orders aren't enforced by FEMA.
"Please be safe and be smart and use your common sense", Cooper added. It was downgraded to a Category 1 hurricane before coming ashore near Wrightsville Beach close to Wilmington, North Carolina.
After blowing ashore as a hurricane with winds of 90 miles per hour (145 kph), Florence virtually parked itself much of the weekend atop the Carolinas as it pulled warm water from the ocean and hurled it onshore.
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It was downgraded to a Category 1 hurricane before coming ashore near Wrightsville Beach close to Wilmington, North Carolina . The NHC said tropical storm-force winds will hit North and SC with full force on Thursday evening.
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About 10mn people could be affected by the storm. The child's injured father was taken to hospital.
At least 14 deaths from the storm have been confirmed, including a man and a woman in Houry County who died from carbon monoxide poisoning. Paramedics trying to reach her were blocked by debris. Officials also said one person was electrocuted in Lenoir County while plugging in a generator in the rain, and a man died after being blown to the ground while checking on his hunting dogs.
In New Bern, North Carolina, one of the cities hardest-hit by the storm that made landfall Friday as a Category 1 hurricane, a beloved bear statue and its thick pedestal were uprooted and washed away. New Bern spokeswoman Colleen Roberts said 455 people had been rescued in the town of 30,000 residents without any serious injuries or deaths.
Drake, along with church member Leroy McGee and a third unidentified church member, had set out in a boat to check homes for anyone needing help, ABC News 4 reports. Some area residents described a harrowing retreat as the storm hit.
"It was pitch black and I was just scared out of my mind", said Tracy Singleton, who with her family later drove through torrential rain and high winds from her home near New Bern.
Almost 814,000 homes in North Carolina and 170,000 in SC are without power.
Cowan said he anxious that the floods would destroy numerous crops that drive the local agricultural economy.
In Jacksonville, North Carolina, next to Camp Lejeune, firefighters and police fought wind and rain as they went door to door to pull more than 60 people out of the Triangle Motor Inn after the structure began to crumble and the roof started to collapse.
In South Carolina, there were 7,000 people staying in shelters.
The federal government's approval late Friday of a major disaster declaration in North Carolina means immediate funds can go to help with damage repairs and recovery for eight coastal counties, Cooper said. Mr Trump, who spoke with state and local officials last Friday, is planning a visit to the region this week.