As of the 11 a.m. Saturday advisory, Florence had maximum sustained winds of 65 miles per hour and was moving to the west at 7 miles per hour.
Gradual strengthening is forecast and Florence could become a hurricane again over the weekend.
Florence was 750 miles southeast of Bermuda and moving west as of 11 a.m. Sunday.
The Center reports that Florence will be a unsafe hurricane near the United States' southeastern coast by late next week as the risk of "direct impacts continues to increase".
The Miami-based weather center says the storm could intensify to a Category 4 hurricane by midweek, but its path was still unclear.
The Navy said all ships in Virginia's coastal Hampton Roads area were preparing to leave port for open seas Monday.
Swells generated by Florence already were impacting Bermuda and starting to reach the U.S. coast, with life-threatening surf and rip current conditions likely, according to the NHC.
North Carolina declared a state of emergency on Friday.
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New York City Mayor Bill de Blasio had been briefed on the incident, his spokesman Eric Phillips wrote on Twitter . Kennedy International Airport in New York City was being quarantined after many passengers reported feeling sick.
At its present course and speed, the center of Florence will likely approach the SC or Georgia coastline on Thursday or Friday.
Forecasters say it's too soon to tell where the storm will go because there's still a lot of uncertainty in its long-term track.
There are now no coastal watches or warnings in effect.
Isaac is forecast to become a hurricane by Sunday evening or Monday.
Virginia and North Carolina and SC already are on alert.
The storm was centred about 875 miles southeast of Bermuda and moving west at 7mph.
Tropical Storm Helene is in the Far Eastern Atlantic, just off the African Coast.
Aircraft data indicate that maximum sustained winds have increased to near 75 miles per hour with higher gusts.
Cooper's emergency declaration makes it possible to waive the state's transportation rules so North Carolina farmers can harvest and transport their crops to market faster.
Helene is forecast to strengthen, with tropical storm conditions reaching the Cabo Verde Islands Saturday.