A hurricane warning is in place for New Orleans from Tropical Storm Isaac, as the city is set to mark the seventh anniversary of its destruction by Hurricane Katrina.
The National Hurricane Center in the US has issued the warning for coastal areas of the states of Florida and Louisiana, including metropolitan New Orleans.
The storm has already left two people dead in Haiti, and forced a one-day delay to the Republican convention.
With winds reaching 95 kilometres per hour, the storm left Haiti and swept across Cuba late on Saturday, with the Miami-based National Hurricane Center reporting it would probably reach Florida within 24 hours.
A hurricane warning was in effect for the Florida Keys and parts of the state's southwest coast and the Republican Party announced that severe weather warnings had prompted a postponed start to its four-day gathering in Tampa.
The proceedings will now start on Tuesday afternoon instead of Monday (local time).
Tens of thousands of Republicans will be in Tampa for speeches, parties and the formal nomination of former Massachusetts governor Mitt Romney as the candidate to take on President Barack Obama in November 6 elections.
Romney said the delay was necessary given the risk to life and limb.
"The safety of those in Isaac's path is of the utmost importance. I applaud those in Tampa making appropriate schedule changes," he said.
Tampa Mayor Bob Buckhorn, a Democrat, had earlier sought to calm jitters about the weather, saying the storm might bring heavy rain to Tampa on the first of the four-day convention but would be followed by sunny skies.
"There may be wet shoes, but every day after Monday ought to be fine," Buckhorn told Fox News.
Vice President Joe Biden canceled a trip to Tampa and other Florida cities because of the approaching storm, Obama's Democratic campaign said.
And in the Gulf of Mexico, BP evacuated its Thunder Horse platform, the world's largest offshore production and drilling facility.
Forecasters earlier said Isaac was near hurricane strength when the eye of the storm passed over Haiti, where hundreds of thousands of people are still living in squalid, makeshift camps following a catastrophic 2010 earthquake.
An eight-year-old Haitian girl died when a wall collapsed at her home and a 51-year-old woman died when her roof collapsed, according to officials. They were the first two known casualties of the storm.
Haiti was the poorest country in the Western Hemisphere even before the earthquake killed 250,000 people, and 400,000 citizens are still living in tent camps in and around the devastated capital Port-au-Prince.
More than 3,300 families had been evacuated to temporary shelters ahead of Isaac as aid groups provided clean water and hygiene kits to try to limit the risk of contaminated water and the spread of disease.
Cuba declared a state of alert in the island's six eastern provinces, where nearly five million people live, and evacuated around 5,000 foreign and local tourists from beachside hotels.