Tropical Storm Fay was expected to move across Haiti on Saturday, the National Hurricane Center said.
The storm, the sixth of the Atlantic 2008 season, had maximum sustained winds near 45 mph with higher gusts, forecasters said.
The storm formed Friday over the Dominican Republic in the Caribbean Sea.
As of 2 a.m. ET Saturday, the center of Fay was about 60 miles east of Port Au Prince, Haiti, and about 260 miles east-southeast of Guantanamo, Cuba.
It was moving west at about 14 mph and was expected to continue moving west-northwest over the next day, forecasters said.
Fay is expected to dump 4 to 8 inches of rain over Hispaniola and eastern Cuba, with possible isolated amounts up to 12 inches, the hurricane center said. Heavy rain could trigger floods and mudslides and raise tides 1 to 2 feet above normal levels in the warning area.
A tropical storm warning is now in effect for the entire coast of Haiti, the hurricane center said.
A tropical storm warning was also issued for the northern coast of the Dominican Republic and for the southern coast east of San Pedro de Macoris, forecasters said. The government of Cuba issued a warning for Guantanamo, Santiago de Cuba and Granma provinces.
A tropical storm warning means tropical storm conditions are expected in the warning area within the next 24 hours.
A tropical storm watch was issued for the Cuban provinces of Holguin and Las Tunas, the hurricane center said. A watch means tropical storm conditions are possible within 36 hours.
Long-range forecasts show the storm reaching the Florida Keys late Monday before heading into the southeastern United States. However, because of the erratic nature of hurricane movement, long-range forecasts often vary from the eventual track.