In Cuba, ex-President Fidel Castro issued an essay mentioning the hurricane and pledging that the government in Havana "guarantees no-one will be forgotten".
At 0800 local time (1200 GMT) on Wednesday the storm's centre was about 150km (90 miles) west of the Haitian capital, Port-au-Prince, and about 195km (120 miles) south-east of Guantanamo province in Cuba, the US National Hurricane Center said.
"Gustav is moving back over water and is expected to regain hurricane strength on Wednesday once it clears the south-western peninsula of Haiti," the NHC said.
The storm lingered for hours over Haiti's poor, deforested southern peninsula on Tuesday, felling trees and raising water levels on banana, bean and vegetable fields.
Hundreds of people in coastal Les Cayes ignored official warnings to seek shelter, instead throwing stones in protest at the high cost of living. UN peacekeepers and Haitian police fired tear gas to disperse the crowds.
Flood victim Marlene Anglade told Reuters news agency: "The water took away our bed, our house ware equipment, and we never received any help at all."
Correspondents say Haiti remains volatile because of soaring food prices, which in April led to deadly protests and the toppling of the nation's prime minister.
Haiti was hit a week ago by a tropical storm that left more than two dozen dead.
Gustav is the seventh tropical storm of the Atlantic hurricane season.
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