Originally Published: 20 SEP 22 03:20 ET

Updated: 20 SEP 22 12:23 ET

By Elizabeth Wolfe, Jason Hanna and Melissa Alonso, CNN

(CNN) -- Hurricane Fiona is threatening more deadly flooding as it slams the Turks and Caicos islands Tuesday, having devastated Puerto Rico -- cutting power and water service for most of its 3.1 million residents -- and leaving more than 1 million without running water in the Dominican Republic.

Fiona, which strengthened early Tuesday to a Category 3 with sustained winds of more than 111 mph, was centered about 40 miles off Grand Turk Island around 11 a.m. ET. Its heavy rains were threatening "life-threatening flooding" through the afternoon in parts of the Turks and Caicos, a British territory of about 38,000 people, the Miami-based National Hurricane Center said.

Still dealing with Fiona's ruinous path are the Dominican Republic -- where Fiona's outer bands still could cause flooding after it traversed the Caribbean nation Monday -- and Puerto Rico, which Fiona crossed a day earlier, causing a near blackout and leaving damage not seen there since Hurricane Maria made landfall five years ago Tuesday, officials said.

Nearly 800 people were brought to safety by emergency workers in the Dominican Republic, according to the country's emergency management director of operations, Juan Manuel Mendez. At least 519 people were taking refuge in the country's 29 shelters Monday, he said.

At least four people have died the severe weather, including one in the French territory of Guadeloupe, which Fiona slammed late last week; two in Puerto Rico; and one in the Dominican Republic, according to officials.

In Puerto Rico, a 58-year-old man was swept away by a swollen river behind his home in Comerío and another man in his 30s died in a fire accident that occurred while he was trying to put gasoline in his generator while it was turned on, officials said.

As of Monday afternoon, at least 1,018,564 customers across the Dominican Republic had no access to running water as 59 aqueducts were out of service and several others were only partially functioning, according to Jose Luis German Mejia, a national emergency management official.

Some in the Dominican Republic were also without electricity Monday as 10 electric circuits went offline, emergency management officials said. It's unclear how many people are impacted by the outages.

Fiona strengthens as it pushes north

Fiona intensified into a Category 3 storm as it moved away from the Dominican Republic's northern coast early Tuesday. Around 11 a.m. ET, it had maximum sustained winds of 115 mph, with higher gusts, according to the hurricane center.

This is the first major hurricane -- Category 3 or higher -- of this year's Atlantic hurricane season.

Heavy rains around the center of Fiona will threaten the Turks and Caicos with "continued life-threatening flooding" through Tuesday afternoon, the hurricane center said.

Those islands could see 4 to 8 inches of rain Tuesday on top of what they received earlier, as well as storm surges -- ocean water pushed onto land -- of 5 to 8 feet, according to the hurricane center.

Hurricane conditions could be seen in Turks and Caicos into Tuesday afternoon, and tropical storm conditions -- winds of at least 39 mph -- were expected to spread over the southeastern Bahamas on Tuesday morning.

Strengthening is expected as Fiona turns from the Turks and Caicos. It could be a Category 4 storm -- sustained winds of 130-156 mph -- by early Wednesday over the Atlantic. It is forecast to pass near or well west of Bermuda late Thursday or early Friday, and could still be at Category 4 when it does, forecasters say.

Over the weekend, Fiona may make landfall in eastern Canada as a hurricane. It is too early to know exactly where or how strong it might be.

Fiona leaves behind devastated Puerto Rico

Fiona's outer bands still were lashing Puerto Rico early Tuesday, soaking regions already struggling under dangerous flooding and destruction.

Parts of the territory will have totaled more than 30 inches of rain from Fiona by the storm's end, the National Hurricane Center said.

Tuesday marks five years since Hurricane Maria's catastrophic landfall and some who lived through the 2017 crisis say Fiona's flooding destruction could be even more severe.

Juan Miguel Gonzalez, a business owner in Puerto Rico, told CNN that his neighborhood had still not finished its recovery from Maria when Fiona struck. But this time, he says, the flooding brought even deeper damage to their homes.

"A lot of people -- more than (during) Maria -- lost their houses now ... lost everything in their houses because of the flooding," Gonzalez told CNN on Monday. "Maria was tough winds. But this one, with all the rain, it just destroyed everything in the house."

Most of the damage inflicted on the island is rain-related, Puerto Rico Gov. Pedro Pierluisi told CNN on Monday evening.

More than 1.17 million of the island's roughly 1.47 million utility customers still were without power as of early Tuesday, according to estimates from PowerOutage.us, which notes updated information on restoration efforts is limited.

Pierluisi said he hopes it will be "a matter of days" to restore power for most customers. Power had been restored to more than 280,000 customers by Tuesday morning, said LUMA Energy, the company that oversees the territory's power grid.

Critically, power was restored to one of Puerto Rico's most vital medical facilities on Monday, according to the territory's health secretary Dr. Carlos Mellado López.

"The power system at all the hospitals in the Medical Center Complex has been restored," Mellado said in a Sunday night tweet. "Our patients are safe and receiving the medical care they need."

Water service also was interrupted for most, because river flooding affected filtration processes and must recede before safe treatment can resume, officials said. On Tuesday morning, about 60% of customers on the island had no running water, the territory's aqueduct and sewer authority said.

Emergency crews battled against unrelenting rain to rescue approximately 1,000 people as of midday Monday, said Maj. Gen. José Reyes, adjutant general of the Puerto Rico National Guard.

In addition to the hundreds of Puerto Rican National Guard members aiding in rescue and recovery efforts, the White House said Monday that President Joe Biden told Pierluisi during a phone call that federal support will increase in the coming days.

"As damage assessments are conducted, the President said that number of support personnel will increase substantially," the White House said.

New York Gov. Kathy Hochul also announced the state would send 100 state troopers to assist relief efforts in Puerto Rico. She also said teams from New York Power Authority are available to help with power restoration.