Weather conditions around the region will deteriorate into the day Friday as Florence slowly comes inland over southeaster North Carolina or near the North Carolina-South Carolina border.
"You put your life at risk by staying", North Carolina Gov. Roy Cooper said.
The Miami-based NHC stressed, however, that while a slow weakening is expected over the next 24 hours "Florence is still forecast to be an extremely risky major hurricane when it nears the U.S. coast late Thursday and Friday".
Southwest Airlines has canceled all its flights in and out of RDU on Thursday and Friday and doesn't plan to resume operations until at least Saturday, according to the airport's website.
Weather Underground meteorology director Jeff Masters said Florence eventually could strike as a Category 1 with winds less than 100 miles per hour (160 kph), but that's still enough to cause at least $1 billion in damage.
Saturday's scheduled game between SC and Marshall has been canceled.
The US may have suffered its most costly year for hurricane damages last year but Florence, the first major storm of the 2018 hurricane season, represents an unusual sort of threat to coastal communities.More news: IPhone Xs Max vs Galaxy Note 9: What Buyers Need to Know
More news: Djokovic, Nadal and Federer in unthinkable three-year first
More news: Hurricane Florence prompts mass evacuations
He said electric power could be out for weeks. Water kills more people in hurricanes than wind, and he said it will still be an extremely unsafe storm for rain and storm surge.
Florence is so wide that a life-threatening storm surge was being pushed 485 km ahead of its eye, and so wet that a swath from SC to OH and Pennsylvania could get deluged.
Incredible time-lapse footage filmed from a hurricane-hunting plane shows what's it's like to fly through the eye of Florence, the storm that's already forced more than 1 million people to evacuate.
Georgia Governor Nathan Deal, concerned the storm would bring its devastation south, issued an emergency declaration for all 159 counties in the state.
All of this has led to fears that the state could face an environmental disaster if industrial waste - including hog manure and coal ash - is washed into people's homes.
Almost 1000 prisoners in SC will not be moved from their cells, despite a mandatory evacuation order in the area. Predictions are for Florence to be far more violent storm.
Marshall: When should we now expect landfall along the coast?
Even with some weakening that's predicted just before it makes landfall, the storm "is expected to remain a risky major hurricane as it approaches the coastline", the hurricane center said.