The storm was centered about 905 miles (1,457 kilometers) east-southeast of Bermuda and moving west at 8 mph (13 kph).
As the storm moves away from the Cabo Verde Islands later Sunday, it was expected to have the opportunity to become a hurricane.
The Miami-based center defines a major hurricane as one with wind speed greater than 110 miles per hour. "Florence is forecast to rapidly strengthen to a major hurricane by Monday, and is expected to remain an extremely unsafe major hurricane through Thursday", the advisory says.
As of the 5 a.m. update from the National Hurricane Center, Florence is still a tropical storm.
Large swells are expected in Bermuda and portions of the East Coast that could cause life-threatening surf and rip currents.
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Hennen said computer models agree Florence is on track to hit the Carolinas.
Forecasters predicted it would become a risky Category 4 storm before a possible landfall Friday.
Florence remains a tropical storm but is forecast to become a hurricane Saturday night as it continues on a westerly track toward the East Coast of the United States, the NWS reports.
North Carolina governor Roy Cooper declared a state of emergency on Friday evening and urged residents to prepare for the worst over the weekend.
Florence is expected to intensify over the next 12-36 hours likely becoming a major hurricane by Monday afternoon.
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Florence's precise path remained uncertain on Sunday, but the NHC said the "risk of direct impact" somewhere between Florida and North Carolina was increasing.
The National Hurricane Center's breakdown of storm strength says Category 3 storms can bring "devastating" destruction.
Behind Florence are two other storms that the National Hurricane Center is monitoring.
Naval Station Norfolk says its employees should not leave their vehicles parked at the sprawling Virginia base in coming days because of the possibility of flooding from approaching Hurricane Florence.
"Our emergency operations center will start up early next week", Knox said, "Because we know that a storm of potentially this size, and potentially of this impact, we as a state need to be in place, on the ground, and ready to help the people of North Carolina".
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