The National Hurricane Center has issued a hurricane warning for southwestern Florida as tropical storm Fay bears down on the state.

Fay has already pounded central Cuba, and claimed up to 35 lives in the Caribbean.

Joe Bastardi, a hurricane forecaster for the Accuweather Center at State College Pennsylvania, told Â鶹´«Ã½net Monday afternoon that Fay is approaching Hurricane strength as it bears down on Florida.

"We're going to see well over 100 to 200 millimeters of rain in southeast Florida," he said.

Bastardi said that the hurricane could cause some tornados to develop as well because of the higher winds.

At 8 p.m. ET Monday, the storm's centre was located about 170 km south of Naples, Fla., and was moving toward the north around 15 km/h. Maximum sustained wind speeds were near 95 km/h, according to the National Hurricane Center.

Fay would reach hurricane strength when winds hit speeds of 120 km/h.

Authorities in the Florida Keys have declared a state of emergency. They have also closed schools, opened shelters and urged visitors to leave. Residents and tourists, however, seemed in no hurry to evacuate.

"We're not worried about it. We've seen this movie before," 58-year-old Willie Dykes, who lives on a sailboat in Key West, told The Associated Press.

Residents are apparently stocking up on supplies like water and plywood, and stores are reportedly running out of some staples.

Bastardi warned that Fay could be a problem for southeast-coast American residents all the way to North Carolina throughout the week if it gains strength if it hits a high system in the Atlantic.

Meanwhile, in Cuba all watches and warnings have ended.

Cuban state media has reported little damage or major flooding so far, but authorities in four provinces evacuated nearly 5,000 residents from low-lying communities and pulled fishing boats from the water. Officials also set up temporary shelters and food distribution centres.

In central Cienfuegos province, officials suspended traditional carnival celebrations. State media said authorities were ready to "protect" the 24,000 foreign tourists in the famous beach resort of Varadero, but provided no more details.

Fay, the sixth named storm of the 2008 Atlantic season, left at least five people dead in Haiti and the Dominican Republic. There are reports from Haiti that another 30 people may have died in a bus crash blamed on the storm.