Dorian became a Category 1 hurricane on Wednesday as it struck the US Virgin Islands, with forecasters saying it could grow to Category 3 status as it neared the US mainland as early as the weekend.
The British Virgin Islands and the Puerto Rican islands of Vieques and Culebra were also in Dorian’s path.
The US territory braced for landslides, widespread flooding and power cuts in its first major test of emergency readiness since the 2017 devastation of Hurricane Maria.
“Dorian brings uncertainty and, for those of us who experienced the storms of 2017, uncomfortable memories,” said Augustus Jaspert, Governor of the British Virgin Islands. “Take heart.”
US President Donald Trump declared a state of emergency on Tuesday night and ordered federal assistance for local authorities.
At 2pm local time, Dorian was over St Thomas in the US territory.
The US National Hurricane Centre said it had maximum sustained winds of 120 kilometres per hour while moving north-west at 20kph.
The centre said the storm could grow into a dangerous Category 3 storm as it pushes in the general direction of Florida.
Dennis Feltgen, one of the centre's meteorologists in Miami, said Dorian might grow in size and could land anywhere from South Florida to South Carolina on Sunday or Monday.
“This will be a large storm approaching the south-east,” Mr Feltgen said.
A hurricane warning was in effect for Puerto Rico, with Dorian expected to dump 10 to 15 centimetres of rain, and 20cm in isolated areas.
It is a forecast that worries many in Puerto Rico, where blue tarpaulins still cover about 30,000 homes nearly two years after Maria.
The island’s 3.2 million inhabitants rely on an unstable power grid that remains prone to cuts since it was destroyed by Maria, a Category 4 storm.
Ramonita Torres, 74, lives by herself in the impoverished, flood-prone neighbourhood of Las Monjas in the capital San Juan.
Ms Torres was still trying to rebuild the home she nearly lost to Maria, but was not able to secure the pieces of zinc that make her roof.
“There’s no money for that,” she said, shaking her head.
A reported 23,000 customers were without power across Puerto Rico by early Wednesday afternoon, said Ángel Figueroa, president of a union that represents electricity workers.
Police said a man, 80, in the northern town of Bayamon died on Wednesday, after he fell trying to climb on to his roof to clear it of debris before the storm hit.
On the US Virgin Islands, which are also struggling to recover from Hurricane Irma, officials were reporting power cuts and light rain by 1.30pm.
“Winds have picked up significantly. We’re starting to get some of those heavier gusts,” said the governor’s spokesman, Richard Motta.
Dorian had earlier been projected to brush the western part of the US territory and the change in the storm's course caught many off guard on the tiny island of Vieques just east of Puerto Rico, a popular tourist destination.
“I’m in shock,” resident Vilma Santana said. Ms Santana said she was relieved it was a storm, not a hurricane.
Mr Trump posted a tweet to reassure locals.
“We are tracking closely tropical storm Dorian as it heads, as usual, to Puerto Rico. The Federal Emergency Management Agency and all others are ready, and will do a great job.”
He took a shot at Puerto Rican officials who accused the government of a slow and inadequate response to Maria.
“When they [FEMA] do, let them know it and give them a big 'thank you'," Mr Trump tweeted. "Not like last time. That includes from the incompetent Mayor of San Juan.”
The Mayor, Carmen Yulín Cruz, tweeted that Mr Trump should "calm down, get out of the way, and make way for those of us who are actually doing the work".
"Maybe Trump will understand this time around this is not about him. This is not about politics, this is about saving lives."
Dorian earlier caused power cuts and blew down trees in Barbados and St Lucia.
Top government officials in Puerto Rico said they were prepared for the storm and had enough equipment, but a couple of mayors, including those in the Al Dhafra, said they did not have enough generators or shelters properly set up.
Jose Ortiz, executive director of the Electric Power Authority in Puerto Rico, acknowledged that the distribution system still had weak areas and could suffer under winds of 80 to 96kph.
But Mr Ortiz said the agency had the needed inventory, including more than 120,000 lights, 23,000 poles and 7,400 transformers.
Freddyson Martínez, vice president of a power workers’ union, told AP that, while the electric grid had improved in some areas, he worried about a lack of power line workers.
The island’s transport secretary said crews were still rebuilding roads damaged by Maria, including more than 1,000 that remain blocked from the storm’s landslides.
Puerto Rico Governor Wanda Vazquez urged those living in flood-prone areas or under tarpaulins to move into one of the island’s 360 shelters.
Officials also said public schools and government offices would remain closed until at least Thursday.
“We learnt our lesson quite well after Maria,” Ms Vazquez said. “We are going to be much better prepared.”
In the US Virgin Islands, Governor Albert Bryan closed schools and government offices.
Mr Bryan said he would introduce a curfew until Thursday, and that officials had opened shelters and prepared sandbags on all three islands.
“The main threat in this storm is the water,” he said early on Wednesday. “We still have a lot of vulnerable people in the territory.”