But help has been slow to come to communities where the devastation is described as "apocalyptic," officials and residents argue.
The governor joined others in emphasizing that Puerto Ricans are American citizens.
"We need something tangible, a bill that actually answers to our need right now," he said. "Otherwise, there will be ... a massive exodus to the (mainland) United States."
Leading Democrats called for swift action to help the island.
Hillary Clinton urged the Defense Department to send a Navy medical ship
, while Democratic House Minority Leader Nancy Pelosi called for Republicans to join with Democrats to pass a robust relief package.
"The Trump Administration must act immediately to make available additional Department of Defense resources for search-and-rescue operations, law enforcement and transportation needs," Pelosi said in a statement. "Our fellow Americans in Puerto Rico and the Virgin Islands deserve to know that their government will be there for them, without question or hesitation."
White House: Response 'anything but slow'
President Donald Trump has pledged federal help for Puerto Rico and the US Virgin Islands. A White House official said Trump is planning to visit Puerto Rico
, but a date has not been set because of infrastructure concerns on the island.
Homeland Security Adviser Tom Bossert and FEMA administrator Brock Long were traveling to Puerto Rico, according to White House press secretary Sarah Sanders.
"The federal response has been anything but slow," Sanders said. "There's been an unprecedented push through of billions of dollars in federal assistance."
Airplanes and ships loaded with meals, water and generators have been arriving or are headed to Puerto Rico and other affected Caribbean islands, the Federal Emergency Management Agency said in a statement. More than 10,000 federal employees are in Puerto Rico and the US Virgin islands helping with research and rescue efforts and moving goods, FEMA tweeted.
In a tweet Sunday, Clinton said, "President Trump, Sec. Mattis, and DOD should send the Navy, including the USNS Comfort, to Puerto Rico now. These are American citizens."
Puerto Rico faces a more immediate danger.
The Guajataca Dam
in the island's northwest corner is releasing water after suffering a "critical infrastructure failure" following the Category 5 storm.
"Some of the dam has fallen apart," Rosselló said. "Now we are making sure that we can assess if the other part will fall down as well. It represents a great danger for about an estimated 70,000 people."
Residents below the dam were told to evacuate on Friday, according to the National Guard. With more than 95% of wireless cell sites out of service, authorities had to physically go to thousands of homes to warn people of the potential collapse.
Rosselló said that while most people in the vicinity had evacuated, efforts were still underway to get people out in peripheral areas.
Without power and communications in much of the island, millions of people have been cut off from the world since Maria hit Wednesday.
"It is as if Puerto Rico got hit with the strength of Irma's winds, leaving a trail of devastation worse than much of the destruction Irma left in Florida," said CNN meteorologist Judson Jones.
"The rainfall in some areas of Puerto Rico rival the amounts of rain left by Harvey in Houston. And now they are contending with a dam disaster that is reminiscent of California's Oroville Dam crisis
earlier this year."
After flying over Puerto Rico on Sunday, CNN's Leyla Santiago said residents could be seen along the highways searching for a cellphone signal.
"The island from above is a completely different color" due to the lack of trees, Santiago said, while pools are filled with black water and debris. The storm ripped the roofs of houses, exposing their interiors to the sky, she said.
Authorities who flew over the island Saturday were also stunned by what they saw. Roads are completely washed away and others are blocked by debris, isolating residents.
"It was devastating to see all that kind of debris in all areas, in all towns of the island," Jenniffer González, the island's nonvoting representative in Congress, told CNN.
At least 10 people have been confirmed killed by the hurricane.
A doctor at Canovanas Medical Center -- one of the few hospitals with a working generator -- said they were running out of fuel to keep it going. Dr. Norbert Seda told CNN that the center only had 2-3 days left of medical supplies and medicine.
None of the three hospitals CNN visited had running water and all said they had just days of supplies left.
However, earlier, Rosselló guaranteed that the people of Puerto Rico would have access to enough food and water to survive.
"We have centers that will distribute water and food, we've already started getting shipments. Today, as a matter of fact, we had a million liters of water come in to Puerto Rico. We have half a million servings of food and other resources." Rosselló also said the island has enough fuel for the next 20 days.
Roselló met with more than 50 mayors and representatives from across Puerto Rico on Saturday. Some said there have been incidents of looting in both homes and stores.