The National Hurricane Center said Florence was expected to slam into the coast around North and SC as a Category 3 or 4 hurricane on Thursday or Friday. Cooper already issued a state of emergency late last week. It was not immediately clear how many people were being evacuated.
If Florence slows to a crawl just off the coast, it could bring torrential rains to the Appalachian mountains and as far away as West Virginia, causing flash floods, mudslides and other unsafe conditions.
The center also spoke about the storm's power.
A hurricane warning is in effect from the South Santee River in SC to Duck, North Carolina.
Virginia Governor Ralph Northam's office predicted "catastrophic inland flooding, high winds and possible widespread power outages", cautioning that the deadliest risk would come from flooding.
Helene, meanwhile, was still in the Atlantic's spawning ground for hurricanes off the coast of Africa, swirling with 105 mph winds and forecast to become a major hurricane, about 375 miles west of the Cape Verde islands.
Expected to make landfall by early morning Friday, most likely along the coast of North Carolina, the impact of the Category 4 storm will be widespread, with destructive winds, life-threatening storm surge, unsafe surf, torrential rainfall, flooding and the potential for tornadoes.
On Sunday, the hurricane center reported that Florence had reached sustained winds of at least 74 miles per hour to be classified a hurricane. The storm is so huge that SC won't be spared even if it escapes the eye of the hurricane.
The National Hurricane Center issued an advisory Monday that the storm is expected to approach the North or SC coast Thursday as an "extremely risky major hurricane". This is the eleventh year on record that the Atlantic has had three or more named storms simultaneously. "The last Atlantic hurricane to intensify as rapidly as far north as Florence's current location was Hurricane Humberto in 2007", he said.
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The Weather Channel has reported that a "destructive strike" on the East Coast of the United States is likely, noting that, if the storm remains a Category 4 hurricane, it will only be the fourth-ever storm of that magnitude to strike the East Coast of the country.
The governors of North and SC and Virginia declared states of emergency far ahead of the approaching storm.
The state has submitted a request to President Donald Trump for a federal disaster declaration, clearing the way for federal money and assistance for any damage from the storm.
North Carolina governor Roy Cooper said his state was "in the bullseye" of the storm.
The storm is expected to reach SC and North Carolina later this week.
"I highly encourage people to move out of the county", Brunswick Emergency Management Director Brian Watts said.
July was wet and August was rather dry which experts say balanced our rain totals for the season but Florence could bring a big shift, depending on its track. "Get ready now", he said.
Hurricane-force winds are extending up to 65 kilometres from the storm's centre, while tropical-storm-force winds are blowing out at up to 240 kilometres.
On North Carolina's Outer Banks, Dawn Farrow Taylor, 50, was gathering photos and important documents and filling prescriptions Monday before heading inland.