Tropical Storm Ernesto moved over water north of Cuba Tuesday and was expected to strengthen before striking Florida, the National Hurricane Center said.
At 8 a.m. ET, Ernesto was about 200 miles (320 kilometers) southeast of Key West and about 215 miles (350 kilometers) south-southeast of Miami in the Florida Straits.
With its 45 mph winds, the storm gained 5 mph overnight and was expected to be near the Florida coastline late in the day as it tracked to the northwest at 14 mph.
Rainfall amounts of up to 10 inches were predicted for southern and eastern Florida by Wednesday.
Tropical storm-force winds extend up to 85 miles from the storm's center, the NHC said.
Ahead of Ernesto's arrival in south Florida, a tropical storm warning and hurricane watch were in effect from Bonita Beach on the west coast, wrapping around the bottom of the peninsula to New Smyrna Beach on the east.
A tropical storm warning is in effect for Guantanamo, Santiago de Cuba, Granma, Holguin, Las Tunas, and Camaguey, Cuba.
While Ernesto is a weak tropical storm, its rains could still cause life-threatening flash floods and mud slides.
"Rainfall amounts of 3 to 6 inches with isolated amounts up to 10 inches are expected over eastern Cuba," the NHC said. "Rainfall amounts of 2 to 4 inches with isolated amounts up to 6 inches are expected over central Cuba."
The warning also remains in effect for Ragged Island and Great Exuma in the central Bahamas, with rainfall amounts of up to 6 inches expected.
Haiti could receive another 3 inches of rain overnight, adding to the island's drenching.
Florida has declared a state of emergency, and residents are stocking up on food, water and fuel. Drivers waited in long lines Monday to fill up gas tanks.
Florida officials ordered tourists to evacuate the Florida Keys on Sunday afternoon, and the area should begin to feel Ernesto's winds early Tuesday.
Monroe County -- which encompasses the Keys -- declared a state of emergency, primarily in order to qualify for state and federal assistance if required.
The Federal Emergency Management Agency has already begun to prepare for Ernesto's possible impact on Florida, FEMA Director David Paulison told CNN Monday.
Paulison canceled plans to join President Bush on a trip to New Orleans to participate in events commemorating Hurricane Katrina, in order to focus on monitoring Tropical Storm Ernesto.
FEMA spokesman Aaron Walker says Paulison "is of greatest value when he is directing the country through a disaster."
FEMA currently has four urban search-and-rescue teams in Florida, as well as 13 medical teams in and around the state on stand-by. The agency has moved supplies into Homestead, outside of Miami, and Jacksonville, in northeastern Florida.
Florida state authorities have not yet requested FEMA assistance but, Paulison said, "We're standing by to be partners with them if they do need that assistance."
The storm prompted NASA to scrub the space shuttle launch set for Tuesday.