Debby, with maximum sustained winds of 45 mph and higher gusts, was about 30 miles south-southwest of Apalachicola, Fla., the National Hurricane Center in Miami said in its 8 p.m. EDT advisory.
The hurricane center said Debby had been nearly stationary for the previous few hours.
"Some slow and possible erratic motion toward the northeast or east-northeast is expected during the next couple of days," the center's advisory stated. "Although Debby has weakened some today, coastal flooding is not yet diminishing. The combination of a storm surge and the tide will cause normally dry areas near the coast to be flooded by rising waters."
A tropical storm warning was in effect for the Florida Gulf Coast from Destin to Englewood.
The Press-Register in Mobile, Ala., reported authorities said a South Carolina man who was swimming in Orange Beach was presumed to have drowned about 1:45 p.m. Sunday in the heavy surf. The search for the unidentified man was suspended about 7:45 p.m.
The News-Press in Fort Myers, Fla., reported the Highland County Sheriff's Office attributed the death of a woman in Venus to severe weather spawned by the off-shore tropical storm. Four homes in the area were destroyed and several others were damaged. The newspaper said it had not been confirmed whether a tornado had touched down.
Debby had the potential to spawn a few tornadoes across portions of the Florida panhandle, peninsula and southern Georgia, the hurricane center said.
Debby is expected to produce a total of 10 to 20 inches of rain over northern and central Florida, with as much as 25 inches possible in isolated areas, forecaster said.
Five to 15 inches of rain could fall over coastal southeastern Georgia and extreme southeastern South Carolina, the hurricane center said.