Puerto Rico Governor Ricardo Rossello called Maria the most devastating storm in a century after it destroyed the US territory's electricity and telecommunications infrastructure.
"Part of the island is lacking communications so what we have are some preliminary assessments about 13 deaths at this juncture," he told CNN early today.
"We're 24 hours post-hurricane warning and right now our efforts are to make sure we have everybody safe, that we can rescue people. Our efforts have already produced almost 700 rescues so we're clearly focused on that."
"We have a lot of flooding, we have reports of complete devastation of vulnerable housing. Of course it's still raining over here."
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Maria was blamed for at least 33 deaths, including 15 in Dominica, three in Haiti and two in Guadeloupe.
"Puerto Rico is absolutely obliterated," US President Donald Trump told reporters yesterday after declaring the territory of 3.4 million people a disaster area, a move that will free up emergency relief funding.
The torrential rain had turned some roads into muddy brown rivers, impassable to all but the largest of vehicles.
Toppled trees, street signs and power cables were strewn across roads that were also littered with debris.
"We all lived through the worst night of our lives, but Puerto Ricans have great inner strength," said Iris Rivera, 53, in San Juan.
"Everyone is helping by cleaning up, directing traffic and supporting their neighbours."
As of early today, Maria was a Category Three hurricane with winds of 125 miles per hour, churning in the sea some 35 miles east of Grand Turk Island in the Turks and Caicos.
The government opened new shelters after several buildings which had been used during Hurricane Irma earlier this month were damaged and authorities feared they might not hold up under another fierce storm.
In the Dominican Republic, the heavy rains triggered flooding as rivers overflowed their banks.
High winds downed trees and electrical pylons, and 140,000 people were left without power, the government said. Some 17,000 have been evacuated from their homes.