Dorian has become an “extremely dangerous” Category 4 hurricane, forecasters said.
The storm’s winds rose to 130mph as Dorian gained new strength while crossing warm Atlantic waters.
The hurricane could strike Florida with even higher winds and torrential rains late on Monday or early on Tuesday, with millions of people in the crosshairs, along with Walt Disney World and US President Donald Trump’s Mar-a-Lago resort.
President Trump declared a state of emergency for Florida as panic buying of food and petrol spread across the state.
Though Dorian is growing in intensity, some of the more reliable computer models predicted a late turn northward that would have Dorian hug the coast, the National Hurricane Centre said.
“There is hope,” Weather Underground meteorology director Jeff Masters said.
The faint hope came on a day in which Dorian seemed to get scarier with each forecast update, and there were fears it could prove to be the most powerful hurricane to hit Florida’s east coast in nearly 30 years.
The National Hurricane Centre’s projected track from Friday showed Dorian hitting near Fort Pierce, some 70 miles north of Mar-a-Lago, then running along the coastline as it moved north.
But forecasters cautioned that the storm’s track was still highly uncertain and even a small deviation could put Dorian offshore or well inland.
Mr Trump declared a state of emergency in Florida and authorised the Federal Emergency Management Agency (FEMA) to coordinate disaster-relief efforts.
He told reporters that “Mar-a-Lago can handle itself” and is more worried about Florida.
As of Friday evening in Florida, Dorian was centred about 575 miles east of West Palm Beach with winds of 130mph.
It was moving northwest at an ever-slower 10 mph (17 kph). Forecasters warned that its slow movement could subject the state to a prolonged and destructive pummelling from wind, storm surge and heavy rain.
Coastal areas could get 15 to 30 centimetres of rain, with 46 centimetres in some places, triggering life-threatening flash floods, the hurricane centre said.
FEMA official Jeff Byard said Dorian is likely to “create a lot of havoc” for roads, power and other infrastructure.
The Bahamas were also in danger, where canned food and bottled water were disappearing quickly and the sound of hammering echoed across the islands as people boarded up their homes.
Dorian was expected to hit by Sunday with the potential for life-threatening storm surge that could raise water levels more than four metres above normal.
“Do not be foolish and try to brave out this hurricane,” prime minister Hubert Minnis said. “The price you may pay for not evacuating is your life.”
In Florida, the governor urged nursing homes to take precautions to prevent tragedies like the one during Hurricane Irma two years ago, when the storm knocked out the air conditioning at a facility in Hollywood and 12 patients died in the sweltering heat.