The storm was headed toward Cuba and then the Alabama-Florida border, forecasters said.
Some rural Jamaicans were cut off by floodwaters hours before the storm was to pass, and authorities planned to fly over the affected southeast area in a helicopter to search for stranded islanders.
Dennis came right behind Tropical Storm Cindy, which made landfall late Tuesday in Louisiana and hindered oil production and refining. Traders said that uncertainty over both storms helped to push oil prices to new highs. Crude oil for August delivery rose $1.69 to settle at $61.28 a barrel and establish a new record on the New York Mercantile Exchange. The previous closing high was $60.54 set June 27.
Packing sustained winds near 70 mph, the fourth storm of the Atlantic season could dump up to 10 inches of rain over mountains in its path, including Jamaica's coffee-producing Blue Mountains, according to the U.S. National Hurricane Center in Miami.
Last year three hurricanes — Frances, Ivan and Jeanne — tore through the Caribbean with a collective ferocity not seen in many years, causing hundreds of deaths and billions of dollars in damages.
A hurricane watch was in effect Wednesday at the U.S. Navy base at Guantanamo Bay, Cuba, where some 520 terror suspects are detained. Inside the detention center, the military prepared audio tapes in at least eight languages warning that a storm was coming and heavy steel shutters would be closed on some cell windows, said Col. Mike Bumgarner.
Military officials had no immediate plans to evacuate troops or detainees at Camp Delta, which is about 150 yards from the ocean but was built to withstand winds up to 90 mph, according to Navy Cmdr. Anne Reese, supervisor of camp maintenance and construction.
Power lines could be knocked down and roofs could be damaged on some older, wooden buildings, Reese said.
"It will be bad, but it's not going to be very destructive," she said.
Meteorologist Chris Hennon said the quadrant threatening Haiti "is typically the worst part of the storm" in terms of wind strength and rains.
Haiti took the deadliest hit of last year's hurricane season when Jeanne, at the time a tropical storm, triggered flooding and mudslides: 1,500 people were killed, 900 missing and presumed dead and 200,000 left homeless.
Poverty-stricken Haitians said there was little they could do about the warnings this time.
"It's not only that we don't have money to prepare, we don't have money either to eat. We are willing to stay here and let whatever happens happen," said Martine Louis-Pierre, a 43-year-old mother of three selling fried food on a street of Port-au-Prince.