It is expected to pass near or over the Turks and Caicos Islands and south-eastern Bahamas late on Saturday or early Sunday.
By then it could be a major hurricane, forecasters say.
Tropical storm Hanna made landfall in the US early on Saturday, dropping heavy rain on beaches near the border between North and South Carolina.
Storm warnings are in force along the Atlantic coast from Georgia to New Jersey.
In Haiti, the devastation from the storm in Gonaives has been described as catastrophic.
Prime Minister Michele Pierre-Louis said her newly-installed government would take the necessary measures to help victims.
Stench of death
Commissioner Dorfeuille told Reuters new agency: "The weather is calm now and we are discovering more bodies. We have found 495 bodies so far and there are 13 people missing.
"The smell of the dead is very unpleasant in Gonaives. The death toll could be even higher."
Hanna dumped massive amounts of rain on the country over four days, blowing down fruit trees and swamping tin-roofed houses.
The port city of Gonaives bore the brunt of the storm, forcing thousands of people to seek shelter on rooftops and balconies as flood waters rose.
The UN's humanitarian co-ordinator in Haiti, Joel Boutrioue, told the BBC it was still difficult to get aid to thousands of people. Roads are cut off and access to some areas is only possible by air - which is limited by the available number of helicopters.
The International Federation of Red Cross and Red Crescent Societies has also launched an appeal, asking for $3.4m in aid.
Haiti was first drenched by Tropical Storm Fay, before Hurricane Gustav wreaked havoc last week, with torrential rainfall over heavily deforested and hilly terrain causing floods and mudslides.
Earlier, Hanna was also blamed for two deaths in Puerto Rico.
In the Dominican Republic, which shares the island of Hispaniola with Haiti, there have been no reports of major damage.
However, preparations are under way for the arrival of Hurricane Ike.
"The ground is saturated and some of the dams in the south-east region are fairly close to their maximum capacity," said meteorological official Gloria Ceballos.
Civil defence director Colonel Juan Manuel Mendez said Dominican troops had been put on alert.
Are you in Haiti? Have you been affected by the storms? Are you based elsewhere in the region? What preparations have you made to deal with the adverse weather? Send us your comments and experiences using the form below.
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