The hurricane, which Puerto Rico governor Ricardo Rossello called "the most devastating storm in a century", had battered the island of 3.4 million people after roaring ashore early yesterday with deadly winds and heavy rain.
The storm was blamed for 10 deaths in the Caribbean, including a man in northern Puerto Rico's Bayamon, who died after being struck by a board he had used to cover his windows, government spokesperson Yennifer Alvarez told AFP.
"If possible, move to higher ground NOW!" the National Weather Service in San Juan said tweeted, calling the flooding "catastrophic".
Puerto Rico was expected to receive 508-762 millimetres of rain through Saturday, with some isolated areas receiving 889 millimetres, the US National Hurricane Center said.
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The rain had turned some roads in the US territory into muddy brown rivers.
As of 5am local time, Maria was a Category III storm on the five-point Saffir-Simpson scale with winds of 185 kilometres per hour. It was churning in the Caribbean Sea about 70 miles north of Punta Cana in the Dominican Republic.
In Puerto Rico, Maria delivered "a lot of flooding, a lot of infrastructure damage, telecommunication system is partially down, energy infrastructure is completely down", Rossello told CNN.
Authorities did not have much information from the island's southeast, which was "virtually disconnected" after taking a direct hit from Maria when it made landfall as a Category-IV storm with winds of more than 240 kmph.
Tens of thousands had fled to shelters. San Juan mayor Carmen Yulin Cruz broke down in tears as she spoke of the utter devastation she had witnessed.
Rossello imposed a 6pm-6am curfew until Saturday and warned of flooding and mudslides.
"I urge the people of Puerto Rico to commit to peace, understanding, and good judgement during these difficult times for our island," he said.
As night fell yesterday, there were reports of looting, and authorities said 10 people have been arrested.
Puerto Rico's most catastrophic hurricane was in 1928 when Hurricane Okeechobee -- also known as San Felipe Segundo -- killed 300 people.
Rossello's assessment for when the lights might come back on was grim. "It depends on the damage to the infrastructure," he told CNN. "I'm afraid it's probably going to be severe. If it is... we're looking at months as opposed to weeks or days."
The US and British Virgin Islands -- still struggling to recover from the devastation of Irma -- are also on alert, along with the Turks and Caicos Islands and parts of the Dominican Republic.
Communications to Dominica have been largely cut, and its airports and ports have been closed.
But an adviser to Prime Minister Roosevelt Skerrit, who spoke to the premier by satellite phone, painted a picture of devastation on the island, where around 73,000 people live.
"It's difficult to determine the level of fatalities but so far seven are confirmed, as a direct result of the hurricane," Hartley Henry said in a statement.
Reports from rural communities spoke of a "total destruction of homes, some roadways and crops," added Henry.
In the French territory of Guadeloupe, one person was killed by a falling tree as Maria hit, while another died on the seafront.
At least two are missing after their boat sank off the French territory, while 40 percent of households were without power.
There were fears that Maria could wreak fresh havoc on islands that were already flattened by Category-V Hurricane Irma earlier in the month.
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