"Laura has become a hurricane with maximum sustained winds of 75 mph (120 km/h), with higher gusts," the US National Hurricane Center reported.
"Significant strengthening is forecast during the next 48 hours, and Laura is expected to be a major hurricane at landfall," it added, warning of storm surges, flooding and torrential rain.
The storm surge "will be accompanied by large and destructive waves" in places, and up to 12 inches (30 centimeters) of rain could cause flash flooding.
On Monday, the storm pounded Cuba unleashing heavy rain and coastal flooding, after killing at least 20 people, including a baby and an eight-year-old child, in Haiti.
The storm also killed four in the Dominican Republic's capital Santo Domingo.
Storms pose a serious risk to Haiti and the Dominican Republic every year from June to November. Heavy rainfall alone can threaten the poorest residents, many of them living in at-risk zones, near canals or ravines that can be obstructed by debris and quickly overflow.
Busy storm season
In Cuba, winds gusting up to 65 miles per hour were reported in the capital Havana on Monday, and waves of more than three meters (10 feet) battered the Maisi area of Guantanamo province.
The high winds tore tin roofs off homes and downed trees as authorities had evacuated at least 160,000 people in the provinces of Guantanamo, Santiago de Cuba, Granma and Camaguey.
The Atlantic storm season, which runs through November, could be one of the busiest ever this year, with the Hurricane Center predicting as many as 25 named storms. Laura is the 12th so far.
Energy companies suspended some oil and natural gas production in the Gulf as the weather deteriorated.
Heavy rainfall and flash flooding also hit Jamaica and the Cayman Islands.
In Petionville, near the Haiti capital Port-au-Prince, torrents of brown water rushing down from mountains caused major damage.
"I didn't know there was bad weather forecast. We don't often have electricity in my neighborhood so I couldn't follow the news on the radio," said Sony Joseph, shivering from the cold.
Tropical Storm Marco -- which also churned through the Gulf of Mexico -- was downgraded from a hurricane and dissipated on Tuesday off the coast of Louisiana before reaching land.
Marco's weakening winds spared the Gulf what would have been twin hurricanes, unprecedented since records began 150 years ago.
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