The U.S. National Hurricane Center says the storm's eye passed close to Grand Turk, the British territory's capital island. The government had imposed a curfew and urged people to flee flood-prone areas, as the storm could raise seas by 5 to 8 feet above normal.
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Fiona had maximum sustained winds of 115 mph and was moving north-northwest at 9 mph early Tuesday, and the Hurricane Center said the storm is likely to strengthen into a Category 4 hurricane as it approaches Bermuda on Friday.
And one day after New York announced it was sending officers and aid to Puerto Rico, New Jersey officials said they would as well.
Paterson Mayor Andre Sayegh and other city officials announced relief efforts for the victims of Hurricane Fiona, saying they have communicated with mayors from Puerto Rico and Paterson's Sister City, Higuey, in the Dominican Republic, regarding the needs of their residents.
Community members are asked to donate non-perishable and hygiene items as well as volunteer their time at the Hurricane Fiona Relief Drive scheduled for October.
The broad storm kept dropping copious rain over the Dominican Republic and Puerto Rico, where a 58-year-old man died after police said he was swept away by a river in the central mountain town of Comerio.
Another death was linked to a power blackout, a 70-year-old man who was burned to death after he tried to fill his generator with gasoline while it was running, officials said.
Parts of the island had received more than 25 inches of rain, and more was falling on Tuesday.
National Guard Brig. Gen. Narciso Cruz described the resulting flooding as historic.
"There were communities that flooded in the storm that didn't flood under Maria," he said, referring to the 2017 hurricane that caused nearly 3,000 deaths. "I've never seen anything like this."
Cruz said 670 people have been rescued in Puerto Rico, including 19 people at a retirement home in the northern mountain town of Cayey that was in danger of collapsing.
"The rivers broke their banks and blanketed communities," he said.
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On Monday, New York Governor Kathy Hochul said she is sending resources to help restore power and help with rescue efforts.
"We will have over 100 troopers from New York State Police Department on their way to Puerto Rico over this next week," she said. "The island of Puerto Rico has had to endure the destruction of the hands of Mother Nature. It's reminiscent of five years ago when we were all just shocked by the scale of devastation on the island. And the images are still very vivid."
New York is also working the Red Cross, SOMOS and other partners to send medical and other supplies, and teams from the New York Power Authority are ready to deploy and assist in restoring power to the island.
"New York knows full well the devastating impact that Mother Nature can bring, and that is why we stand ready to help the people of Puerto Rico recover and rebuild from this terrible storm," Hochul said. "Our brothers and sisters in Puerto Rico are incredibly resilient but, in times like this, New York will be there to help in any way we can, including sending personnel and resources to help the island and its residents recover."
WATCH: Gov. Hochul announces relief in the wake of Hurricane Fiona
Gov. Hochul pledges assistance in the wake of Hurricane Fiona
The blow from Fiona was made more devastating because Puerto Rico has yet to recover from Hurricane Maria, which destroyed the power grid in 2017. Five years later, more than 3,000 homes on the island are still covered by blue tarps.
Authorities said Monday at least 2,300 people and some 250 pets remained in shelters across the island.
Fiona triggered a blackout when it hit Puerto Rico's southwest corner on Sunday, the anniversary of Hurricane Hugo, which slammed into the island in 1989 as a Category 3 storm.
By Tuesday morning, authorities said they had restored power to more than 285,000 of the island's 1.47 million customers. Puerto Rico's governor, Pedro Pierluisi, warned it could take days before everyone has electricity.
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Water service was cut to more than 837,000 customers - two thirds of the total on the island - because of turbid water at filtration plants or lack of power, officials said.
Fiona was not expected to threaten the U.S. mainland.
In the Dominican Republic, authorities reported one death: a man hit by a falling tree. The storm displaced more than 12,400 people and cut off at least two communities.
The hurricane left several highways blocked, and a tourist pier in the town of Miches was badly damaged by high waves. At least four international airports were closed, officials said.
The Dominican president, Luis Abinader, said authorities would need several days to assess the storm's effects.
Fiona previously battered the eastern Caribbean, killing one man in the French territory of Guadeloupe when floodwaters washed his home away, officials said.
The Associated Press contributed to this report.
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