Tropical storm warnings have been issued for the southern Florida coast, the Cayman Islands and parts of Cuba and the Bahamas as a new tropical depression approaches.
The National Hurricane Center in Miami says the depression has maximum sustained winds Tuesday near 35 mph, and is very close to tropical storm strength.
At 2:00 p.m. ET the depression was located about 160 miles south of Havana and moving north-northwest near 10 mph.
In Florida, the tropical storm warning is in effect for Jupiter Inlet southward to East Cape Sable, Florida Bay and the Florida Keys.
The warning also covers the northwestern and central Bahamas.
In Cuba, the storm's projected path would take it directly over the Cuban capital and surrounding provinces.
Cuba's chief meteorologist said the weather system was large but disorganized and the heaviest rains were expected to hit east of the storm's center in an area from Matanzas to Las Tunas in eastern Cuba.
"This is a very weak system," Jose Rubiera said. He forecast that top wind speeds would rise to no more than 50 mph. "Those winds will not cause any damage, except possibly to sensitive crops or weak structures."
He said he was more concerned about the rains, which could be intense in some areas.
While the 2010 Atlantic hurricane season has been unusually active, Tuesday's storm is the first to directly threaten Cuba. The island was devastated by three hurricanes in 2008, but was entirely spared last year.
Serious damage from a hurricane this year could be a major blow to the cash-strapped government as it attempts to right its weak economy. This month, Cuba's communist leaders announced that a half-million state employees would be laid off and reforms implemented to allow more private enterprise.