The first hurricane of the season claimed its first victims in Haiti where a bridge in the southwestern town of Grand Goave collapsed.
It threatened to intensify as it makes a beeline for Cuba and then landfall in the Gulf of Mexico projected Sunday or Monday, raising fears oil supplies will be disrupted by the fourth storm in as many weeks.
Dennis is a "dangerous hurricane" that looks to strengthen to near 130 mph within 12 hours, the U.S. National Hurricane Center in Miami warned. It should pass over central Cuba within 24 hours, it said.
Thunderstorms covered all the Dominican Republic, southern Haiti and northeast Jamaica. Cayman Islands and Cuba also were under hurricane warnings, including the U.S. detention camp holding some 520 terror suspects in Guantanamo Bay.
The southern Florida Keys went on hurricane warning Thursday afternoon and ordered tourists to flee, and the southern Florida peninsula was on tropical storm watch, expecting stormy conditions within 36 hours.
CBS News Correspondent Mark Strassmann reports that from Louisiana to Florida, residents are bracing for a possible hit, just days after being soaked by Cindy, which is still causing trouble all along the Eastern Seaboard. People are especially nervous in places like Pensacola, which is still rebuilding from Ivan's destruction last September.
In Haiti, wind gusts uprooted a palm tree and flung it into a mud hut, killing one person and injuring three in southern Les Cayes town, the Red Cross said. The collapsed of the bridge also killed an unknown number of people, said officials who spoke on condition of anonymity.
Rivers burst their banks in the dangerously deforested country.
In Jamaica, where a man narrowly escaped from a car swept away by fast-moving floodwaters Wednesday night, Prime Minister Percival Patterson urged people in low-lying areas to evacuate.
"Let us all work together in unity so that we will be spared the worst," he said in a national radio broadcast.
But only about 1,000 of the 2.6 million people were in shelters late afternoon, when local forecasters said the eye of the storm was passing 50 miles north of Port Antonio, on Jamaica's northeast coast.
Cuba began evacuating more than 2,500 tourists and workers from Cayo Largo del Sur, in the string of keys along the southeast, the National Information Agency reported. Livestock also was taken to higher ground.
Most tourists were taken to other hotels in Havana and Varadero beach resort in the north.
Thousands of students at government boarding schools in the southeast were being sent home.
There were no immediate plans to evacuate detainees or troops from the U.S. detention center's Camp Delta at Guantanamo Bay, on Cuba's extreme southeast end, Gen. Jay Hood said in an interview.