The storm's sustained winds reached 75 mph, just over the threshold for a hurricane, as it made its way across the Atlantic, about 750 miles southeast of Bermuda, the National Hurricane Center said.
The storm's center was on track to pass between Bermuda and the Bahamas on Wednesday, the NHC said.
The Miami-based center said that it was still too early to predict the hurricane's exact path but that a huge coastal area from SC to the mid-Atlantic region should prepare for a major strike late in the week.
In South Carolina, Charleston city officials were offering sandbags for residents to fill.
"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 in a statement on Sunday.
In southeast Virginia, Naval Station Norfolk told its employees they should not leave their vehicles parked at the sprawling base in coming days because of the flood threat.
On Friday, Gov. Roy Cooper declared a State of Emergency, making it possible to waive the state's transportation rules so North Carolina farmers can harvest and transport their crops to market faster. It's expected to strengthen through Tuesday before beginning to weaken.
Carnival Horizon which is the newest Carnival Cruise Ship has now canceled its scheduled port of call in Puerto Rico due to Florence which is now a category 1 Hurricane. All university-sponsored events and athletics, including Fall Family and Alumni Weekend (Sept. 14-15), the women's soccer match vs. ECU on Thursday (Sept. 13) and the Hampton Inn Seahawk Invitational women's volleyball tournament (Sept. 14-15) are canceled.
Authorities in the Carolinas are warning residents to prepare for a potential disaster as Hurricane Florence gains strength ahead a potential landfall later in the week.
Across the Southeast, people were urged to put together emergency supply kits, prepare their homes and research evacuation routes.
North Carolina Governor Roy Cooper also urged his state's residents to get ready, noting the storm already was generating swelling waves and risky currents along the coast. Forecasters predicted it would become a unsafe Category 4 storm before a possible landfall Friday.
McMaster said he had asked President Donald Trump to declare a federal emergency in SC in anticipation of the storm's arrival.
Hurricane Isaac formed Sunday and, as a Category 1, became the fifth hurricane of the season.
Forecasters say Tropical Storm Florence has turned into a hurricane and is swirling toward the East Coast for what could be a direct hit toward the end of the week.
By 11 p.m. Sunday, Florence was moving across the Atlantic Ocean at about 7 miles per hour, and it was almost a Category 2 hurricane, with peak winds of 90 miles per hour.
The storm's maximum sustained winds are near 110 km/h with higher gusts.
Florence's predicted path, as of early Monday morning.