Category 4 hurricane is most powerful storm in Caribbean since 2007
The US is preparing to evacuate its base at Guantanamo Bay in Cuba over the threat from Hurricane Matthew.
The base, notorious as the site of a detention facility for captives from the Afghanistan war, is in the current predicted path of the storm.
Category 4 Matthew, the most powerful storm in the Caribbean since 2007, is making its way north with 150mph (240kph) winds.
Its centre is now expected to miss Jamaica but to barrel across southwest Haiti before smashing into eastern Cuba, where Guantanamo is situated.
Jamaica is still forecast to suffer up to 25 inches (63cm) of rain, while Haiti could receive up to 40 inches (101cm).
The US National Hurricane Center said the rain is likely to trigger life-threatening landslides and floods.
The latest forecast has Matthew hitting southern Haiti at 8pm (EDT) on Monday and reaching Cuba about 12 hours later.
Haiti has started evacuating residents of small, exposed sandy islands in the south who want to leave.
Albert Moulion, Haiti's interior ministry spokesman, said: "We have already started evacuations," he said. "The national center of emergency operations has been activated."
The US Navy said about 700 spouses and children are due to be airlifted to Florida from its base on Cuba to wait until the storm passes by.
A spokesman said in a statement: "The remaining military and civilian personnel will shelter in place and be able to support recovery efforts once safe to do so following the storm's passage."
The Dominican Republic also issued a tropical storm warning.
The NHC said: "Maximum sustained winds remain near 150 mph... with higher gusts. Hurricane-force winds extend outward up to 25 miles (35 km) from the center, and tropical-storm-force winds extend outward up to 205 miles (335 km).
"Matthew is forecast to remain a powerful hurricane until it interacts with the high terrain of Hispaniola (Haiti and Dominican Republic) and eastern Cuba in about 48 hours or so.
"Once Matthew reaches the Bahamas, the upper-level environment and warm waters will favor some restrengthening."
It is feared the storm could move on to affect the Bahamas and the east coast of the United States, although the path is difficult to predict.
Countries likely to be affected are fearful of the effect it could have on their economies.
In Jamaica, which has been suffering a long economic slowdown, there are worries the hurricane could affect tourist destinations such as Montego Bay in the island's north.
Many continued to prepare for the worst, buying up supplies and battening down windows and doors.
One shopper in Jamaica's capital Kingston, weather forecaster Ennis St Patrice, told Reuters: "We've had these kind of occurrences in the past and it is generally bad, because Jamaica does not have proper infrastructure.
"In simple rainfall, we have flooding."