President Donald Trump declared Puerto Rico a disaster zone and said Maria had "obliterated" the US territory of 3.4 million people.
Governor Ricardo Rossello called Maria the most devastating storm in a century and said the island suffered a total breakdown of its electricity and telecommunications infrastructure.
Rossello warned that expected heavy rainfall over the next few days could cause deadly flooding and mudslides.
"The biggest concern is the amount of rain and flooding, particularly in the west," Rossello told WAPA radio. "We expect up to 25 inches (63cm) from the tail of the hurricane."
The storm has been blamed for at least 21 deaths, including 15 in Dominica, two in Guadeloupe and one in northern Puerto Rico’s Bayamon district, where a man was struck by a board he had used to cover his windows.
In Haiti, three deaths were blamed on the storm: a drowning and two people struck by lightning.
"Puerto Rico is absolutely obliterated," Trump told reporters on Thursday after declaring the island a disaster area in a move that will free up emergency relief funding.
"Puerto Rico is in a very, very, very tough shape," he said.
Though the storm had moved back out to sea, authorities declared a flash flood warning for all of Puerto Rico as the torrential rains continued to lash the island.
"If possible, move to higher ground NOW!" the National Weather Service station in San Juan said in a tweet, calling the flooding "catastrophic".
The rain had turned some roads in the US territory 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.
Although Maria had passed over Puerto Rico and lost some of its power, it was still packing winds gusting at up to 125 miles per hour (210km per hour).
As of Thursday evening it was moving as a Category 3 hurricane offshore along the northern coast of the Dominican Republic.
It is forecast to head near or just east of the Turks and Caicos Islands and southeastern Bahamas Thursday night and on Friday, the National Hurricane Center in Miami said.
In the Dominican Republic, rains from Maria triggered flooding as rivers overflowed their banks. Fierce 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.
Ricardo Ramos, who heads Puerto Rico’s electricity board, said it could take months before power is fully restored on the island.
"The system... has been totally destroyed," he said of the electricity grid.
While the island had suffered major blackouts from previous hurricanes, Ramos said the impact would be felt much more keenly this time.
"I guess it’s a good time for dads to buy a glove and ball and change the way you entertain your children and the way you are going to go to school and the way you are going to cook for gas stoves other than electric," Ramos told CNN.
In San Juan, where tens of thousands rode out the storm in shelters or else hunkered down in their homes, residents told of their terrifying ordeal.
"This was absolutely the worst experience we’ve had with a hurricane," Kim Neis, an American who has lived on the island for 30 years, said.
"None of the others were anything like as intense as this."
Governor Rossello imposed a 6pm to 6am curfew until Saturday.
There were reports of looting and authorities said 10 people had been arrested.
Maria has already torn through several Caribbean islands, claiming the highest toll on Dominica, which remains largely cut off from the outside world.
"So far, we would have buried in excess of 15 people," Dominica’s Prime Minister Roosevelt Skerrit said on television.
"If there (are) no other fatalities, it is a miracle," Skerrit said.
"It has been brutal. I saw almost complete devastation," said Skerrit, who has made several flights over the territory of some 72,000 people.
"We have no water, no electricity, very limited communications," he said.
"It is worse than a war zone," said Skerrit, who himself had to be rescued during the hurricane, which blew the roof off his residence, source from Vietnamnews.