Some forecast models also give the storm a chance of strengthening into a tropical storm, which is classified as having sustained winds between 39 and 73 miles per hour.
The weather service also issued a tropical storm watch for the Alabama-Florida border Sunday afternoon.
A tropical storm warning is in effect for the Alabama-Florida border westward to east of Morgan City, Louisiana. The storm will gain strength as it crosses the Gulf of Mexico, though not enough to become a hurricane, according to the National Hurricane Center. The deluge could cause flash floodings in some areas.
A tropical storm warning and a storm surge watch are in effect for Harrison, Hancock and Jackson counties and parishes in southeast Louisiana, according to the National Weather Service in New Orleans.
The system could dump 2 to 4 inches (5-10 centimeters) of rain over parts of the Bahamas, the Florida Keys and South Florida through early Tuesday.
Tropical storm force winds, heavy rain with isolated flooding, and an isolated tornado threat are all possible tomorrow as a tropical wave strengthens into a tropical storm over the next 24 to 36 hours. Conditions look favorable for tropical storm development as the system moves towards the north central Gulf coast. Additional strengthening is forecast within the next 48 hours.
In addition to Florence, forecasters also are watching a tropical wave located that's just emerged off the west coast of Africa.
The tropics are getting active just in time for the peak of Atlantic hurricane season on September 10.
Florida governor Rick Scott tweeted that Floridians and those visiting the state should monitor the weather as they plan Labor Day festivities.