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MIAMI, Florida (CNN) -- Ernesto weakened to a tropical storm Sunday afternoon, the National Hurricane Center said, but forecasters warned the storm could regain hurricane status as it moved toward Cuba.
A hurricane watch was issued for all of the Florida Keys from Ocean Reef to the Dry Tortugas, meaning that hurricane conditions are possible within the area generally within 36 hours.
Additional hurricane watches may be issued for portions of the Florida peninsula Sunday night, the hurricane center said in its 5 p.m. advisory.
At 8 p.m., Ernesto's center was located just off Haiti's southwestern peninsula and about 140 miles south-southeast of Guantanamo, Cuba. Its top winds had dropped to 50 mph, and it was moving northwest at 7 mph.
If it continues to follow that track, the storm will be near eastern Cuba's southern coast by Monday morning, the weather center said.
Ernesto is forecast to strengthen as it moves away from Haiti and could regain hurricane status by the time it reaches Cuba, the weather center said.
One computer model has the storm crossing from eastern Cuba to southeast Florida, and another has it going over Cuba, through the Florida Straits and into the extreme southeast Gulf of Mexico before turning northeast, National Hurricane Center Director Max Mayfield said.
"The tricky part is when that turn to the north really occurs," he said.
Though Ernesto's precise track may be uncertain, "It certainly looks like it's going to impact a significant portion of Florida before it's all over," he said.
The longer the storm stays over Cuba, the more it would weaken, he said. (Watch Mayfield illustrate the storm forecast -- 4:49)
A hurricane warning remains in effect for the southwestern peninsula of Haiti from its border with the Dominican Republic westward to Haiti's southernmost tip, where torrential rains were pouring.
The most immediate concern with the storm is with rainfall over Haiti and the Dominican Republic, Mayfield said.
"They have a real problem with flash floods and mud slides in those areas," he said.
Forecasters said rainfall amounts of 6 to 12 inches -- with isolated amounts of up to 20 inches possible -- are expected over Haiti, the Dominican Republic and parts of Cuba.
A hurricane warning remains in effect for the Cuban provinces of Guantanamo, Santiago de Cuba, Granma, Holguin, Las Tunas and Camaguey. A hurricane warning means that hurricane conditions are expected in the warning area within 24 hours.
Officials in Florida called on tourists to evacuate the Florida Keys, which should begin to feel Ernesto's winds early Tuesday. The Florida Division of Emergency Management said early Sunday afternoon that forecast changes "now make Ernesto a direct threat to the Keys and peninsula."
Monroe County -- which encompasses the Keys -- declared a state of emergency, primarily in order to qualify for state and federal assistance if required. A mandatory visitor evacuation was issued for all the Florida Keys at 1 p.m. Sunday.
"Travelers with immediate plans to travel to the keys must postpone trips until the threat of Ernesto ends and officials provide a directive reopening the keys for travelers," the Florida Division of Emergency Management said in a written statement.
People with travel trailers and recreational vehicles were ordered to leave immediately, and state and county parks were set to close Sunday afternoon.
As of 6 a.m. Monday, the Monroe County Emergency Operations Center is to be activated and special-needs patients are to be taken to a shelter at Florida International University.
Key West International Airport was expected to remain open through Monday night, Monroe County Airports Director Peter Horton said.
Satellite image from 10:15 p.m. ET Sunday shows Ernesto over Haiti and the Dominican Republic, southeast of Cuba.
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