Fay could start pelting parts of the Keys and south Florida as soon as Monday.
The National Hurricane Center in Miami said a hurricane watch was in effect for the Florida Keys from south of Ocean Reef to Key West, and along the mainland from Card Sound Bridge west to Bonita Beach.
The sixth storm of the 2008 Atlantic season picked up some momentum early Sunday morning as it headed toward Cuba, and could be a hurricane by the time it reaches the island's center, forecasters said.
Officials issued a mandatory evacuation order for visitors starting at 8 a.m. Sunday, and asked tourists who had not yet arrived to postpone their trips.
"We hate to inconvenience those visitors that had plans to be in the Keys the next few days, but their well-being is our top priority," said Monroe County Mayor Mario Di Gennaro, chairman of the Keys tourist development council.
Florida Gov. Charlie Crist declared a state of emergency Saturday because Fay "threatens the state of Florida with a major disaster," he wrote in an executive order.
A tropical storm watch was also in effect for the southeast coast of Florida from Ocean Reef north to Jupiter Inlet, as well as for Lake Okeechobee.
Keys emergency officials often take the precaution of ordering early evacuations when a storm threatens because traffic can back up for miles on the single highway to Florida's mainland.
Besides the threat of damage from high winds, most of the islands sit at sea level and could be flooded by Fay's storm surge. Flooding from the storm on Saturday killed four people in the Dominican Republic and Haiti.
At 8 a.m. EDT Sunday, Fay's center was located about 395 miles southeast of Key West and moving west-northwest at 13 miles per hour. The storm had maximum sustained winds near 50 mph with some gusting.
State officials in Tallahassee opened their emergency operations center, said Blair Heusdens, a spokeswoman for the state's Division of Emergency Management.
"We like to have the executive order in place before the storm," Heusdens said. "That way we can have our resources ready."
Tourists and locals still packed downtown Key West on Saturday, seemingly unfazed by the approaching storm.
Todd Hitchins, 36, of Big Pine Key, about 30 miles east of Key West, said he planned to stock up on water and propane for his grill but wasn't too worried.
"This will be good practice," mused Hitchins, who said he's lived here during much more powerful storms. "But you've got to be prepared, be ready."
Jeff Emmett, operations manager at Fairfield Inn and Suites in Key West, said Saturday afternoon the hotel had no cancellations or early check-outs.
"Bu Chris Celestina, 24, was sitting at the hotel's poolside bar while on vacation with four friends from Pennsylvania.
"We're not really worried," Celestina said as he ordered a drink. "Whatever happens, happens. If we get evacuated, that will definitely put a damper on our plans, but until we have to, we're not moving."
Some Keys residents were preparing for the aftermath.
Andrew Cardwell, 26, filled up nine 5-gallon gas cans for his employer, Pirate Scooter Rentals, early Saturday afternoon.
"As soon as the storm passes through, people are going to want to rent mopeds," Cardwell said. "We're just getting it while we can."