The storm's maximum sustained winds increased to 75 mph, just above the threshold for a hurricane, said the U.S. National Hurricane Center in Miami.
Ernesto could grow into a Category 3 hurricane by Thursday, menacing a broad swath of the Gulf Coast including hurricane-ravaged New Orleans, the hurricane center said earlier. Category 3 Hurricane Katrina struck the city a year ago Tuesday.
New Orleans residents were told Saturday that the partially repaired levee system . Many residents – who lived through Katrina – are already preparing to evacuate the city if Ernesto heads toward Louisiana.
"It's over nice warm Caribbean waters, and far enough off the coast of Haiti that it is still strengthening now," said Ron Goodman, a forecaster a the center.
The storm, moving northwest at 10 mph, was projected to make landfall in Haiti on Sunday afternoon, dropping heavy rain that could cause deadly mudslides in the heavily deforested Caribbean country. Ernesto was expected to cross west-central Cuba on Tuesday night before continuing into the Gulf of Mexico.
"There will be probably be a restrengthening after it leaves the Cuban coast to a Category 2, and Wednesday night it will be west of Fort Myers as Category 3. That's the current thinking," Goodman said.
Haiti issued a hurricane warning for its southern coast, and hurricane watches were in effect for Jamaica and the Cayman Islands.
Cuban Civil Defense has placed the western and central areas of the island on hurricane watch, reports CBS News producer Portia Siegelbaum.
Jamaica's Prime Minister Portia Simpson Miller put the country's security forces on alert and said at a news conference Saturday that all the island's shelters were open.
"Ensure that the children are not left alone, and make it easier for rescue workers," she said.
Jamaica issued advisories by radio and television for residents in low-lying areas across the island to be prepared to evacuate if necessary.
At 5 a.m. (0900GMT), the fifth named storm of the Atlantic hurricane season was centered about 120 miles southwest of Port-au-Prince, Haiti, and 255 miles southeast of Kingston.
Heavy showers hit Kingston on Saturday afternoon, causing traffic jams as motorists tried to reach stores. People waited in long lines at supermarkets, filling grocery carts with canned goods, batteries and candles.
"It's nature and we can't stop it from taking its course," said taxi driver Patrick Wallace, 55, as he left a supermarket after stocking up on canned goods.
In Haiti, emergency officials went on local radio to warn people living in flimsy shantytowns on the southern coast to seek shelter in schools and churches. The hurricane center said Haiti and the Dominican Republic could get up to 20 inches of rain in some places — which could cause life-threatening flash floods and mud slides.
"These people could be in great danger," said Adel Nazaire, a coordinator with Haiti's civil protection agency. "Flooding is the biggest concern because a lot of residents live along the rivers and the sea."
Despite a delay in the launch of the space shuttle Atlantis Saturday, Ernesto a potential lift off early in the week, but it could cause problems if Atlantis doesn't launch until later in the week.