Tropical Storm Isaac unleashed heavy rain and winds off Puerto Rico and the Virgin Islands as it moved across the Caribbean Thursday and could strengthen into a hurricane before tearing across the Dominican Republic and Haiti.

Isaac also posed a threat to Florida, where it is forecast to pass near the state's Gulf Coast on Monday as the Republican National Convention starts in Tampa, Reuters reported.

Authorities have not ruled out postponing or relocating the Republican convention if the storm takes direct aim at Tampa. But Craig Fugate, director of the Federal Emergency Management Agency, told CNN the convention was not his biggest concern, at least for now.

"People are spending a lot of time talking about that," Fugate said of the convention. "I wish they'd be talking about making sure people in the Keys are getting ready and that people in southwest Florida are getting read."

The U.S. National Hurricane Center said said Isaac was centered about 190 miles south-southwest of San Juan, Puerto Rico, Thursday evening and was moving westward at 16 miles per hour. The storm had top sustained winds of 45 mph. The center said Isaac could become a Category 1 hurricane Friday as it nears Hispaniola but might weaken after passing over Haiti toward Cuba.