The storm, about 750 miles southeast of Bermuda, is projected to make landfall early Friday morning somewhere in the Carolinas, according to National Hurricane Center forecasts.
Virginia has declared a state of emergency Saturday in anticipation of Tropical Storm Florence and its potential impact, according to a statement from Gov. Ralph Northam. One, Hurricane Florence, is already cause 85-mph winds expected to become an "extremely dangerous" major hurricane.
Most of the projected paths show Florence making landfall in North Carolina.
The storm's center will approach the U.S. Southeast coast on Thursday after passing between Bermuda and the Bahamas on Tuesday and Wednesday.
Unsafe swells generated by Florence were expected to batter Bermuda early in the week, as well as parts of the U.S. Eastern Seaboard.
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.
A third storm, Helene, off the Cabo Verde Islands was expected to become a hurricane later on Sunday.
Forecasters said it is too early to know the exact path Florence will take but warned that it could roll ashore in the Carolinas by Thursday.
Loewenthal said the waters off the North Carolina coast are in the mid-to-upper 80s, which would allow the storm to maintain its strength. Monday is the climatological peak date of hurricane season, the height of the eight-week period when the most powerful storms usually form, CNN meteorologist Pedram Javaheri said.
Officials along North Carolina's coast are issuing a mandatory evacuation order for all visitors and residents on Hatteras Island as Hurricane Florence moves closer to the East Coast.
Henry McMaster declared a state of emergency Saturday to give his state time to prepare for the possible arrival of a hurricane.
Meanwhile, two other tropical storms have formed in the Atlantic Basin. Gradual strengthening is forecast and Florence could become a hurricane again over the weekend.
Hurricane Florence was raised to Category 3 Monday as it approaches the Carolinas coast.
At right, off the coast of Africa is Tropical Storm Helene, and second from right is Tropical Depression 9.
The United States faced a series of high-powered hurricanes past year, including Hurricane Maria, which killed some 3,000 people in Puerto Rico, and Hurricane Harvey, which killed about 68 people and caused an estimated $1.25 billion in damage when it brought catastrophic flooding to Houston.