Tropical Storm Gustav has made landfall over Jamaica, with meteorologists warning it could strengthen into a hurricane "at any time".
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At 1400 EDT (1800 GMT) Gustav was just 65km (40 miles) east of Kingston and moving slowly towards the capital.
It is expected to head towards the US, prompting evacuation preparations in New Orleans, three years after the city was devastated by Hurricane Katrina.
Haitian officials say 51 people have died since the storm struck on Tuesday.
At least eight more deaths were reported after Gustav tore through the Dominican Republic.
Heavy rain and winds began lashing eastern parts of Jamaica as the storm struck, tearing roofs off buildings and uprooting trees.
Workers were being evacuated from oil rigs in the Gulf of Mexico, as oil prices on trading markets rose amid forecasts Gustav could threaten oil installations in the region.
'Possible hurricane'
The Miami-based US National Hurricane Center (NHC) forecasts Gustav will strengthen in the coming hours as it creeps westwards at around 7km/h.
The Jamaican government issued a hurricane warning before Gustav came ashore, packing maximum sustained winds of 110km/h (70mph), with some higher gusts.
A hurricane is defined by winds of 119km/h (74mph), according to the NHC.
Emergency officials there have set up shelters and dispatched relief supplies to flood-prone areas.
On Friday, the storm is expected to move towards the Cayman Islands, where a hurricane watch is also in effect.
Across the islands, non-essential government employees were sent home on Thursday afternoon ahead of the storm's expected arrival on Friday afternoon.
Cayman Airways added 25 extra flights to their schedules in an effort to evacuate tourists and residents wanting to get off the islands.
But officials said they were not expecting a significant storm surge for Grand Cayman - which came as a welcome relief to islanders as much of the island sits just metres above sea-level.
New Orleans prepares
Cuba has replaced a hurricane warning for its eastern Granma province with a tropical storm warning.
The NHC warns that Gustav is also expected to produce heavy rainfall - up to 25 inches (64cm) in some places - over Jamaica and the Caymans.
"These rains will likely produce life-threatening flash floods and mud slides," it said.
Meanwhile, the US state of Louisiana and New Orleans are making their own preparations ahead of Gustav's arrival.
Meteorologists say the storm could make landfall in the US anywhere from south Texas to Florida by Tuesday.
Louisiana Governor Bobby Jindal has declared a state of emergency and activated the National Guard.
New Orleans has also begun planning a possible mandatory evacuation, hoping to prevent the chaos it saw after Katrina, which struck the city three years ago on Friday.
Gustav is the seventh tropical storm of the Atlantic hurricane season.