The latest in a series of hurricanes and tropical storms in the Atlantic is heading for the Bahamas.
The storm caused extensive damage in the Dominican Republic
Tropical storm Jeanne is "very near" Great Inagua Island packing winds of 50mph (85km/h) - which are expected to strengthen, forecasters say.
Jeanne has killed eight people in the Dominican Republic and Puerto Rico and forced hundreds to leave their homes.
It is unclear if it will hit the US, where operations have begun to assess the deadly impact of Hurricane Ivan.
Forecasters warn that the hurricane season is far from over - even as millions of people are trying to recover from the havoc wreaked in the past five weeks.
Up to 33 people are reported to have been killed by Ivan in the US, in addition to about 70 in the Caribbean with Grenada, Jamaica and the Cayman Islands worst hit.
At 2100 GMT on Saturday, tropical storm Jeanne was moving at speeds of 7mph (11km/h) - a pace it was expected to maintain in the next 24 hours, the US National Hurricane Center said.
"Storm surge flooding of one to three feet (30-90cm) above normal tide levels is possible in the south-eastern Bahamas," the centre said.
Between nine and 13 inches (22.9-33cm) of rain were expected.
It said a tropical storm warning remained over a number of areas including the Turks and Caicos Islands.
The storm reached the Dominican Republic on Thursday as a hurricane, with winds near 80mph (129km/h), before weakening - and then strengthening again.
It had raged through Puerto Rico on Wednesday, bringing up to two feet (60cm) of rain and flooding hundreds of homes.
President George W Bush has cancelled campaigning this weekend to observe relief work in Alabama and Florida.
He declared Alabama, Mississippi and Louisiana disaster areas as the authorities counted the cost of Hurricane Ivan.
Curfews were ordered in the worst-hit areas, while thousands of National Guard members were sent to help with rescue efforts and to curb looting.
Florida already had the status of disaster area after being hit by hurricanes Charley and Frances over the past six weeks.
Ivan crashed into the Gulf Coast on Thursday, hitting a swathe of territory from Florida to Louisiana with winds of up to 165mph (265km/h).
A series of destructive tornadoes spun off, ripping homes apart and flooding streets. The victims included an eight-year-old girl who died when a tree fell on her house.
Electricity remains unavailable in much of the Florida panhandle, because of damage to power lines.
In neighbouring Alabama, more than 750,000 homes and businesses are also without power.
The Red Cross aims to support 85,000 people over the next six months in Grenada, Jamaica, the Cayman Islands and Cuba.