"Maria is forecast to remain an extremely dangerous Category 4 or 5 hurricane while it approaches" the British and US territories late today, the NHC said.
Arriving just as islanders in the region are struggling to recover from devastating Hurricane Irma which struck earlier this month, Maria claimed its first victim in the French territory of Guadeloupe, where two other people were missing.
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On neighbouring Dominica, premier Roosevelt Skerrit posted on Facebook that there were initial reports of "widespread devastation" and that the roof of his own home had been blown off.
"We have lost all what money can buy and replace," he said.
The airport and ports have been closed on the tropical island of 72,000 people.
St Martin, a French-Dutch island that was among the worst hit by Irma with 14 dead, was under a maximum "violet" alert, with people ordered to stay indoors.
A similar measure was in place in the British Virgin Islands.
"Our islands are extremely vulnerable right now," the territory's premier Orlando Smith said in a statement, warning that the storm could turn debris left by Irma into dangerous projectiles.
Guadeloupe was serving as a base for aid flights to Irma-hit French territories after the hurricane, and there were fears that major damage there could hamper the relief operation.
Authorities said there were few reports of damage to buildings so far, though several areas around the largest city Pointe-a-Pitre were flooded and fallen trees were blocking many roads.
Some 40 percent of households in the territory of 400,000 are without power.
"Everything around me is shaking," former French minister Victorin Lurel told BFMTV from his home in the south of the island.
The Dominican Republic, whose east coast was battered by Irma, ordered citizens in part of the north to evacuate ahead of Maria's arrival.
St Kitts and Nevis, the British island of Montserrat, Culebra and Vieques are also on alert.
Britain, France and the Netherlands boosted resources for the Caribbean ahead of the storm, after facing accusations that they were ill-prepared for the damage done by Irma in their overseas territories.
"We are planning for the unexpected, we are planning for the worst," said Chris Austin, head of a UK military task force set up to deal with Irma.
France said 110 more soldiers would be deployed to the region after widespread complaints of looting and lawlessness on St Martin after Irma.
Building supplies were hurriedly flown in to help islanders repair roofs torn off by Irma as Maria approached.
Irma left around 40 people dead altogether in the Caribbean before churning west and pounding Florida, where the death toll stood at 50 yesterday.
It broke records when it whipped up winds of 295 kilometres per hour for more than 33 hours straight.
French President Emmanuel Macron, speaking in New York where he is attending the UN General Assembly, said the lethal sequence of hurricanes is "one of the direct consequences of global warming".
The French leader said he had spoken to US President Donald Trump about the issue earlier today.
Macron hosted Trump in Paris in July when he sought to persuade the US leader to reconsider his decision to pull out of the Paris climate accord.
Many scientists are convinced that megastorms such as Irma, and Harvey before it, are intensified by the greater energy they can draw from oceans that are warming as a result of climate change.
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