But the window of opportunity is closing.
"There's still time ... but people need to move fast," Ricardo Rosselló told CNN's "Anderson Cooper 360˚," calling the storm the "worst hurricane in modern history in Puerto Rico."
US President Trump tweeted his thoughts to those on the island, a US territory. "Be careful, our hearts are with you," he wrote, calling the storm a "monster hurricane," and pledging assistance.
Maria is a Category 5 storm with sustained winds of 175 mph (281 kph). By late Tuesday, the eye of hurricane was expected to move near or over St. Croix in the US Virgin Islands and make landfall in Puerto Rico Wednesday morning.
"Winds are starting to pick up, the glass is starting to bow back and forth. We're soon going to take shelter in a safe room," Mike Theiss, a hurricane chaser who is staying in Fajardo, told CNN's Don Lemon.
Maria has already obliterated parts of Dominica and killed at least one person in Guadeloupe.
Rosselló said there are about 500 shelters open. Emergency workers are still out, but will head in when sustained winds reach 50 mph, the governor said.
Many people live on the eastern half of Puerto Rico, which forecasters worry will endure the brunt of the most powerful hurricane ever to hit the island.
Residents of Puerto Rico, who were spared some of Irma's wrath when that hurricane's core passed north of the island, boarded up homes and businesses Tuesday. People who fled to the US territory as Maria, and before it, Hurricane Irma, which swept through the region just days ago, advanced on their islands sought refuge in hotels and shelters.
Jessica Mangiaracina and Bob Perkins came to San Juan from St. Thomas with their two children. Irma destroyed everything around them and threw the island into chaos.
It took them six days to get off St. Thomas, they said, killing chickens for food and making their way through areas being looted.
They got to Puerto Rico by catamaran, where, like many others, they tried to get a flight out with no success.
Now they are coping with the reality that they've escaped into the middle of Hurricane Maria's angry path.
The couple is among thousands of people in shelters.
When asked what their current plan is, Perkins responded, "survive."
Heather Farrell, a visitor to the island, is on her honeymoon with her husband Luke. They were married on September 9. She says that they had tried to cut their trip short when it became apparent that they were in Maria's firing line.
"We did try to get off, as early as Saturday but all flights were either booked or canceled. We actually are on the ocean -- our room faces the ocean. It's pretty windy but there is no rain. We'll stay inside for now."
She said that hotel staff had asked that all guests that are staying at the hotel come downstairs early Wednesday morning to a safe room that they have set up for them.
"I would rather be home than here but I guess we're making the best of it," she said.
Worst storm in almost 80 years
Millions of Puerto Ricans are hoping to survive what could be the most powerful storm to ever hit the island. Maria likely will be the first Category 4 or 5 hurricane to make landfall in Puerto Rico in more than eight decades.
"No generation has seen a hurricane like this since San Felipe II in 1928," Rosselló said earlier. "This is an unprecedented atmospheric system."
President Donald Trump said the federal government will aid Puerto Rico in the aftermath of the storm.
"Puerto Rico being hit hard by new monster Hurricane," the President tweeted. "Be careful, our hearts are with you -- will be there to help!"
Maria has already killed one man in Guadeloupe after he ignored orders to stay inside and was struck by a falling tree, the island's government said.
Man killed by falling tree in Guadeloupe
Two other people are missing after a boat sank off the coast of La Désirade, a smaller island near the mainland of Guadeloupe. The government said about 80,000 people, or 40% of the households on the island, are without power.
The storm also caused "widespread devastation" in Dominica, Prime Minister Roosevelt Skerrit said Tuesday.
The hurricane shredded the prime minister's house overnight and left much of the island -- population 73,000 -- in ruins.
Overseas, relatives were trying to reestablish contact with loved ones on the island.
Petrona Joseph, a public relations consultant who lives in Montreal, told CNN that her sister in Dominica was at home in Roseau, huddling in the bathroom with the rest of the family when they lost their roof.
They thought about trying to go to a neighbor's home but the winds were too strong. Joseph last heard from her sister by text Monday night around 11 p.m.
Maria is now the strongest hurricane on record to make landfall in Dominica, a former French and British colony whose economy relies heavily on tourism and agriculture.
Puerto Rico says Maria 'will be catastrophic'
Maria could bring up to 2 feet of rain and a storm surge of up to 9 feet to Puerto Rico, sparking flooding and mudslides, CNN Meteorologist Allison Chinchar said.
In the capital city of San Juan, residents cleared store shelves of water and other supplies.
A CNN producer who was driving from the airport Tuesday said there were still some vehicles on the road. Of the two gas stations she passed, one was open. Many shops were already closed, she observed.
Some tourists from California told her that the hostel they are staying at moved them to an interior room when the men were unable to find flights home.
Gov. Rosselló has declared a state of emergency, and Trump has issued an emergency declaration for Puerto Rico to aid with federal assistance.
Puerto Rico sheltered many of the evacuees who fled from other Caribbean Islands during Hurricane Irma earlier this month. Now those evacuees and native Puerto Ricans are bracing for devastation.
"This is an event that will be damaging to the infrastructure, that will be catastrophic," Rosselló said. "Our only focus right now should be to make sure we save lives."
"We expect to feel storm winds, tropical storm winds, (from) Tuesday up until late on Thursday. That's about two-and-a-half days of tropical storm winds," Rosselló said.
The Puerto Rico Convention Center in the capital San Juan to the north -- which is still housing Hurricane Irma evacuees from other Caribbean islands -- is preparing to accept thousands of residents as the worst of the storm is felt.
Martinique largely spared
One bit of good news emerged from the Caribbean: The French island of Martinique suffered no major damage, the French Interior Ministry tweeted Tuesday.
Maria knocked out power to about 50,000 homes, and 10,000 homes had no water. But overall, the damage assessment was "reassuring," the French Interior Ministry said.
The director general of French civil security, Jacques Witkowski, said only two people on Martinique suffered minor injuries.
In just 30 hours, Maria's intensity exploded from 65 mph on Sunday to 160 mph by Monday night, the National Hurricane Center said.
The British Foreign Office said more than 1,300 troops are on standby, either on affected islands or in nearby locations, ready to help after Maria tears through.
One military team has been deployed to the British Virgin Islands, and a British military reconnaissance team is on standby to go to the British territory of Montserrat.
The HMS Ocean is set to arrive in the area at week's end with 60 tons of government supplies.