Hurricane Irma will “devastate” either Florida or neighbouring states, the head of the US federal emergency agency has said.
Brock Long said parts of Florida would be without power for days. Half a million people in the state have been ordered to leave their homes.
Hurricane Irma has left a trail of destruction in the Caribbean, affecting an estimated 1.2m people.
At least 20 people are known to have died so far.
It has been downgraded to a category four storm, but officials warn that it remains “extremely dangerous”.
The US National Weather Service says that Irma was expected to bring wind speeds of around 165mph (270km/h) over the weekend as it hits Florida.
“Hurricane Irma continues to be a threat that is going to devastate the United States in either Florida or some of the south-eastern states,” Mr Long said.
“The entire south-eastern United States better wake up and pay attention,” he added.
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The death toll continued to rise on Friday in the Caribbean.
France’s Interior Minister Gérard Collomb said nine people were dead and seven missing in the French territory on St Martin, an island shared with the Netherlands, and St Barthélemy, known more commonly as St Barts. Another death – the second – has been confirmed in the Dutch territory of Sint Maarten.
French officials said six out of 10 homes on Saint-Martin were so badly damaged that they were uninhabitable.
The US Consulate General in Curacao said it believes an estimated 6,000 Americans are stranded on the island.
French, British and Dutch military authorities have deployed aid – including warships and planes equipped with food, water and troops – to their territories.
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Reporting from another badly damaged island, Barbuda, the BBC’s Laura Bicker says the destruction there is worse than feared.
Where is Irma – and where next?
The storm, which most recently lashed the Turks and Caicos islands and brought torrential rain to the Dominican Republic and Haiti, was headed towards Cuba and the Bahamas.
The worst of the storm is expected to hit east and central Cuba, with the eye of the storm predicted to pass between the north coast of Cuba and the Bahamas, the National Hurricane Center (NHC) said.
About 50,000 tourists are fleeing or have fled Cuba, with resorts on the north coast now empty, Reuters reports.
A huge evacuation of south-eastern, low-lying coastal areas in the Bahamas has been ordered. The tourism ministry said in a video statement that thousands of tourists left before the storm’s arrival.
Meanwhile Mr Long predicted a “truly devastating” impact on Florida.
South Florida “may be uninhabitable for weeks or months” because of the storm, the US National Weather Service said.
On the archipelago of Turks and Caicos, with its population of about 35,000, one witness described a drop in pressure that could be felt in people’s chests.
Irma ripped off roofs on the capital island, Grand Turk, flooded streets, snapped utility poles and caused a widespread black-out.
Governor John Freeman told the BBC that people in low-lying areas were evacuated and sent to shelters. The islands’ highest point is only 50m (163ft).
Irma also caused some damage to roofs, flooding and power outages in the northern parts of the Dominican Republic and Haiti.