The Center also warned that "Florence is expected to be an extremely unsafe major hurricane through Thursday".
Like Hurricane Harvey, which stalled over Texas in 2017, Florence could linger over the Southeast for several days after landfall.
Cooper and his counterparts in South Carolina, Virginia and Maryland all declared states of emergency.
The center of Florence was forecast to sweep between Bermuda and the Bahamas on Tuesday and Wednesday before making its assault on the US coast.
A forecast from the hurricane center projected that Florence will pick up speed in the coming days.
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Hurricane-force winds extend outward up to 30 miles from the center and tropical-storm-force winds extend outward up to 140 miles. Writing on Twitter , he added: 'Take time right now to call your friends and family who live in the Carolinas and Virginia.
"Everyone in North Carolina needs to keep a close eye on Florence and take steps now to get ready for impacts later this week", Cooper said.
Beyond the damage from wind and high surf, Hurricane Florence is predicted to slow over the Carolinas where it may dump up to 30 inches of rain over much of North and SC. Florence was a Category 4 storm late afternoon Monday.
Hurricane Florence is bearing down on the East Coast, bringing 105 miles per hour winds and a risk of flooding.
As of 5 p.m. ET Monday, the center of Florence was located about 1,170 miles from Cape Fear, North Carolina, and was moving to the west-northwest at 13 mph.
All inland residents should find out now if you live in a flood prone area.
The hurricane, which strengthened to a Category 4 on Monday, is expected to intensify as it approaches the Carolinas, said John Quagliariello with the National Weather Service.
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N.H.C. said Isaac is a small hurricane.
The governor warned residents that Florence was gaining strength and that the winds would likely be higher than other recent hurricanes. A "Hurricane Hunter" aircraft recorded maximum sustained winds of 130 miles per hour.
WILMINGTON - Hurricane Florence is now a Category 4 hurricane, according to the National Hurricane Center. Water, not the wind, will probably be the biggest threat.
At 0300 GMT Issac was about 1,305 miles east of the Windward Islands - a region still recovering from last year's powerful Hurricane Maria - with winds of 75 miles per hour. We're just a strip of land - we're a barrier island.
Florence appears to have weakened slightly but is expected to restrengthen later on Tuesday, the NHC said.
"There is an increasing risk of two life-threatening impacts from Florence: storm surge at the coast, freshwater flooding from a prolonged and exceptionally heavy rainfall event inland, and damaging hurricane-force winds", the NHC warned.
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