The storm's sustained winds reached 75 mph, just over the threshold for a hurricane, on Sunday morning as it was swirling across the Atlantic, about 750 miles southeast of Bermuda. It was moving west at 6 mph.
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The National Hurricane Center says it is still too early to predict the hurricane's exact path, but a huge coastal area from northern Florida to North Carolina should prepare for a major hit.
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If the storm does move inland, central North Carolina could get torrential rainfall and sustained tropical storm winds plus the risk for tornadoes.
Governors in both South Carolina and Virginia declared a state of emergency Saturday to give their states time to prepare for the possible arrival of the storm. South Carolina Gov. Henry McMaster emphasized that there's no way to know yet when and where the storm will hit land, or when evacuations might be called.
On Friday, North Carolina Gov. Roy Cooper declared a state of emergency and urged residents to use the weekend to prepare for the possibility of a natural disaster.
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"We are entering the peak of hurricane season and we know well the unpredictability and power of these storms," Cooper said.
The State Emergency Operations Center will activate Monday at 1 p.m.
"Everyone in North Carolina needs to keep a close eye on Florence and take steps now to get ready for impacts later this week," Gov. Cooper said. "State emergency management, transportation, health experts and others are making sure North Carolina is prepared for the storm, and I urge the public to review your emergency plans and gather your supplies now."
Swells generated by Florence are affecting Bermuda and starting to reach parts of the Eastern Seaboard, the National Weather Service said.