The Miami Herald reported Isaac was blamed for the deaths of at least nine people, including seven in Haiti and two in the Dominican Republic.
At 11 p.m. EDT, the center of Isaac was centered about 75 miles west-southwest of Key West and about 510 miles southeast of the mouth of the Mississippi River as it moved into the eastern Gulf of Mexico, the National Hurricane Center in Miami said.
The storm was sporting sustained winds of 65 mph with higher gusts and was moving west-northwest at 14 mph. Tropical storm-force gales were extending 205 miles out from its center.
U.S. forecasters said a hurricane warning was in effect for east of Morgan City, La., to Destin, Fla., including New Orleans, Lake Pontchartrain and Lake Maurepas.
A hurricane watch was in place for east of Dustin to Indian Pass, Fla.
A tropical storm warning was ordered for the Florida Peninsula from Jupiter Inlet southward on the state's east coast and from Tarpon Springs southward on the west coast. The hurricane center discontinued its tropical storm warning for the east coast north of Jupiter Inlet.
A tropical storm warning also was out for the Florida Keys, Lake Okeechobee and from east of Destin to the Suwannee River.
The hurricane center said watches or warnings may be extended westward along the Louisiana coast early Monday.
Isolated tornadoes will be possible over central and southern Florida through Monday, the forecasters said.
Dangerous surf and rip current conditions will continue in the northwestern Bahamas, the Florida Peninsula and the Florida Keys during the next day or so, as well.
Isaac was forecast to make a gradual turn to the northwest and to slow its forward speed over the next couple of days. That track would take the storm away from the Florida Keys Sunday night, over the eastern gulf Monday and approaching the northern gulf Tuesday.
Forecasters said they expect Isaac to strengthen and become a hurricane in a day or two.
Organizers of the Republican National Convention in Tampa announced Saturday the convention activities Monday were canceled and events would begin Tuesday because of Isaac's threat.
Isaac, which already doused Cuba, was expected to begin drenching the Tampa area Sunday and gusty winds would begin early Monday, the National Weather Service said.
The Office of Civil Protection in Haiti said the seven people killed in the Caribbean island nation included a young man buried in a landslide in DonDon, a 7-year-old boy electrocuted in the Artibonite Valley, a woman killed by a falling tree in Jacmel and a 10-year-old girl in Thomazeau, the Herald said, while police in the Dominican Republican said two men drowned in rain-swollen rivers.
Many thousands of people were left without power on the island, as well.
"We've lived through this before. We're not afraid," Lucien Pierre, a 28-year-old mother of two, told the Miami newspaper as she washed clothes outside her tent. "We'll pray and watch."