The latest projected path of Ernesto shows the storm veering east after it moves through Cuba and striking Florida as a possible Category 3 storm.

"Computer models are in better agreement that the storm will cross over Florida as at least a Category 2 or 3 storm," Local 6 meteorologist Michele Cimino said. "Central Floridians now need to begin to get prepared for the worst."

Sunday's path brings the storm through Central Florida which would bring us flooding rains and dangerous winds.

"This storm has the potential to be a major hurricane by the time it reaches Florida Thursday," Cimino said.

The National Hurricane Center in Miami said the storm could grow by Thursday into a hurricane as strong as Katrina, which struck the city a year ago Tuesday.

"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 at 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 country. Ernesto was expected to cross west-central Cuba on Tuesday night before continuing into the Gulf of Mexico.

Ernesto was expected to bring rain and wind to southern Florida by early Tuesday, and the hurricane center encouraged people in southern Florida, the Florida Keys and Mexico's Yucatan Peninsula to monitor the storm. It was projected to strengthen off western Florida on Wednesday but the location of any U.S. landfall was unclear.

Emergency officials in Haiti evacuated some residents low-lying areas in the northwest city of Gonaives, which was devastated by Tropical Storm Jeanne in 2004.

The storm was expected to pass Sunday afternoon near the tip of Haiti's southwestern peninsula, where officials said there was heavy rain but no reported damage. "There's no plan to evacuate now but if there's more rain later we may have to," said Adel Nazaire, coordinator with Haiti's civil protection agency.

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.

In Cuba, the Communist Youth newspaper Juventud Rebelde warned Cubans of heavy rain, winds and potential flooding on the southeast coast starting Sunday night. Cattle were moved to higher ground, and workers cleaned gutters and picked rubble off the streets ahead of the storm.

At 2 p.m., the fifth named storm of the Atlantic hurricane season was centered about 105 miles southwest of Port-au-Prince, Haiti, and 165 miles south-southeast of Guantanamo Bay, Cuba. It was moving northwest at about 9 mph.

The Royal Caribbean cruise line said it was diverting three ships scheduled to depart the United States on Sunday and Monday, sending them to alternative Caribbean ports to avoid the storm.

The hurricane center said the storm's 75 mph winds pushed it just above the threshold for a Category 1, the weakest category of hurricane. To reach Category 3, Katrina's strength, the winds would have to reach at least 111 mph.

"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.

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."

Watch Local 6 News for more on this story.