Irma - which has killed at least 19 people and devastated thousands of homes in the Caribbean - made landfall late yesterday on the Camaguey Archipelago of Cuba as a maximum- strength Category 5 storm.
The hurricane weakened slightly to a Category 4 hours later, swirling some 245 miles (395 kilometers) away from Miami and packing still powerful maximum sustained winds of 155 miles per hour, according to the US National Hurricane Center.
More than a million people on the Caribbean's largest island have evacuated as a precaution, authorities said.
Irma is expected to strike the Florida Keys late today and tomorrow before moving inland, and many residents have joined a mass exodus amid increasingly dire alerts to leave.
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"Irma remains an extremely dangerous hurricane!" tweeted the National Weather Service early today.
"It's not too late to get off the Keys!!!" the agency said. "You still have time, this morning, to get out! Please, the Keys are not safe."
Warning that Irma would be worse than Hurricane Andrew - which killed 65 people in 1992 - Florida's governor said all 20.6 million Floridians should prepare to flee.
"If you're in an evacuation zone, you should be very cautious, you should get out now," Governor Rick Scott told CNN. "This is a powerful storm bigger than our state."
Bumper-to-bumper traffic was snaking north out of the peninsula, with mattresses, gas cans and kayaks strapped to car roofs.
"It is frightening," he told AFP at a shelter in Miami. "We had to leave without a cent, without taking a bath, or bringing anything."
The storm ravaged a series of tiny islands before slamming into the Virgin Islands and Puerto Rico.
French state-owned reinsurer CCR estimated Irma had caused 1.2 billion euros (USD 1.4 billion) worth of damage to homes, vehicles and businesses in the territories of Saint Martin and Saint Barts.
"Houses are smashed, the airport is out of action," Saint Barts resident Olivier Toussaint told AFP.
Meteorologists meanwhile were closely monitoring two other Atlantic storms.
Jose, another powerful Category 4 storm, was heading towards the same string of Caribbean islands Irma has pummeled in recent days.
Katia made landfall in eastern Mexico late yesterday - just as the country was grappling with its worst earthquake in a century - as a Category 1 hurricane.
It was later downgraded to a tropical storm but was still bringing rains that could bring "life-threatening flash floods and mudslides.