(CNN) Nearly a week after Hurricane Maria slammed Puerto Rico, the US commonwealth looks something like this: Most homes are without power and phone service, with little hope of having it restored soon. Food and medicine are dwindling, especially for those isolated by impassable roads. And rescuers still are finding and removing desperate people from their demolished communities.

It is, in short, a humanitarian crisis, San Juan's mayor told CNN on Tuesday.

"We are finding dialysis patients that haven't been able to contact their providers, so we are having to transport them in near-death conditions," Mayor Carmen Yulín Cruz said, recalling a group's visit to two San Juan-area nursing homes this week. "We are finding people whose oxygen tanks are running out, because ... small generators now don't have any diesel."

Customers wait in line for power generators at a store in San Juan on September 18.

Customers wait in line for power generators at a store in San Juan on September 18.

People buy provisions in Petit-Bourg, Guadeloupe, as the hurricane approached on Monday, September 18.

People buy provisions in Petit-Bourg, Guadeloupe, as the hurricane approached on Monday, September 18.

Soldiers patrol a street in Marigot, St. Martin, as preparations were made for Maria on September 19.

Soldiers patrol a street in Marigot, St. Martin, as preparations were made for Maria on September 19.

A motorist drives on the flooded waterfront in Fort-de-France, Martinique, on September 19.

A motorist drives on the flooded waterfront in Fort-de-France, Martinique, on September 19.

Cars line up at a gas station in San Juan on September 19.

Cars line up at a gas station in San Juan on September 19.

A boat is overturned off the shore of Sainte-Anne, Guadeloupe, on September 19.

A boat is overturned off the shore of Sainte-Anne, Guadeloupe, on September 19.

People in Luquillo, Puerto Rico, board up windows of a business on September 19.

People in Luquillo, Puerto Rico, board up windows of a business on September 19.

People stand near debris at a restaurant in Le Carbet, Martinique, on September 19.

People stand near debris at a restaurant in Le Carbet, Martinique, on September 19.

A street is flooded in Pointe-a-Pitre, on the French Caribbean island of Guadeloupe, on September 19.

A street is flooded in Pointe-a-Pitre, on the French Caribbean island of Guadeloupe, on September 19.

Waves crash in San Juan as the hurricane neared Puerto Rico on September 19.

Waves crash in San Juan as the hurricane neared Puerto Rico on September 19.

Two girls play on cots at the Humacao Arena.

Two girls play on cots at the Humacao Arena.

Members of a rescue team embrace as they wait to help in Humacao on September 20.

Members of a rescue team embrace as they wait to help in Humacao on September 20.

Trees are toppled outside the Roberto Clemente Coliseum in San Juan on September 20.

Trees are toppled outside the Roberto Clemente Coliseum in San Juan on September 20.

Rescue vehicles are trapped under an awning in Humacao on September 20.

Rescue vehicles are trapped under an awning in Humacao on September 20.

Residents move aluminum panels from an intersection in Humacao on September 20.

Residents move aluminum panels from an intersection in Humacao on September 20.

Power lines are scattered across a road in Humacao, Puerto Rico, on September 20.

Power lines are scattered across a road in Humacao, Puerto Rico, on September 20.

San Juan is shrouded in darkness after the hurricane knocked out power to the entire island of Puerto Rico.

San Juan is shrouded in darkness after the hurricane knocked out power to the entire island of Puerto Rico.

People walk through the destruction in Roseau on September 20.

People walk through the destruction in Roseau on September 20.

Damage is seen in Roseau, Dominica, on September 20.

Damage is seen in Roseau, Dominica, on September 20.

A mattress that fell from the third floor is surrounded by debris outside a San Juan apartment complex on September 20.

A mattress that fell from the third floor is surrounded by debris outside a San Juan apartment complex on September 20.

A gas station's sign is damaged in Punta Cana, Dominican Republic, as the hurricane passed just north of the country on September 21.

A gas station's sign is damaged in Punta Cana, Dominican Republic, as the hurricane passed just north of the country on September 21.

A man walks on a highway divider while carrying his bicycle through San Juan, Puerto Rico, on Thursday, September 21.

A man walks on a highway divider while carrying his bicycle through San Juan, Puerto Rico, on Thursday, September 21.

People collect water from a natural spring created by landslides in Corozal, Puerto Rico, on Sunday, September 24. Puerto Rican Gov. Ricardo Rosselló said the island faces a humanitarian crisis.

People collect water from a natural spring created by landslides in Corozal, Puerto Rico, on Sunday, September 24. Puerto Rican Gov. Ricardo Rosselló said the island faces a humanitarian crisis.

An aerial view shows the flooding in San Juan on September 25.

An aerial view shows the flooding in San Juan on September 25.

Yancy Leon rests at the Luis Muñoz Marin International Airport near San Juan on September 25. She's been waiting in line for two days to get a flight out.

Yancy Leon rests at the Luis Muñoz Marin International Airport near San Juan on September 25. She's been waiting in line for two days to get a flight out.

An apartment building is missing a wall in San Juan, Puerto Rico, on Monday, September 25, nearly a week after Hurricane Maria devastated the US commonwealth. Power is still out in most places, and communications remain almost nonexistent on the island of 3.4 million people.

An apartment building is missing a wall in San Juan, Puerto Rico, on Monday, September 25, nearly a week after Hurricane Maria devastated the US commonwealth. Power is still out in most places, and communications remain almost nonexistent on the island of 3.4 million people.

Searchers are trying to visit every structure in the capital area, she said.

"Our bodies are so tired, but our souls are so full of strength, that we will get to everyone that we can get to," Yulín Cruz said.

Two people died in an intensive care unit in a San Juan hospital after it ran out of diesel, Yulín Cruz said. Their causes of death weren't immediately available. It wasn't clear whether those deaths were among the at least 16 deaths that Karixia Ortiz, spokeswoman for the Puerto Rico Department of Public Safety and Vilmar Trinta, spokesperson of Puerto Rico's Police superintendent, attributed to the storm.

Maria struck September 20, knocking out power for nearly all the 3.4 million residents and demolishing structures on an island already struggling after Hurricane Irma's brush earlier this month.

Nearly 1.6 million electric customers in Puerto Rico are without power, according to the Federal Emergency Management Agency and Energy Department, not counting those using generators as a backup.

Even before the hurricane hit, the island's electrical grid was functioning with "Band-Aids," Héctor Pesquera, the territory's public security secretary, told CNNE.

President Donald Trump said Tuesday he will visit Puerto Rico on October 3, just as he inspected damage and rescue efforts in Texas and Florida after recent hurricanes in those states.

JUST WATCHED See the hardest-hit areas of Puerto Rico Replay More Videos ... MUST WATCH See the hardest-hit areas of Puerto Rico 02:33

Residents in remote areas are stranded with shrinking supplies, and some haven't been able to contact their families to tell them they survived.

Coffee growers Gaspar Rodriguez and Doris Velez said the food they had left has spoiled.

"You work, work and work, and it's for nothing," Rodriguez said after losing everything.

Rescuers still are "removing people from hazardous conditions -- (people who) are ill, that can't move on their own," said Carl Levon Kustin, a FEMA task force leader from California.

"We've been working feverishly to get out to these areas," Kustin said Tuesday.

Puerto Rico Gov. Ricardo Rosselló told CNN that more support and resources for the island are needed.

While crediting the Trump administration and FEMA for responding "quickly" and "appropriately," Rosselló said, "There are some challenges and we need more resources."

'We have not lost our faith'

Near the town of Utuado, Rosario Heredia, 56, who is diabetic, is in her house, which is spewing water from every corner. She reaches high into her closet for a piece of clothing and squeezes water from it like a soaked sponge.

Heredia had hoped that help would've arrived by now -- but it hasn't.

Trees are broken and twisted on the island, leaving behind a wasteland. Roads have washed away, and others are blocked by debris.

After losing everything, some Puerto Ricans say the only thing they have left is their faith.

"Really, we are people who serve God," Wilfredo Villegas said. "And yes, we are saddened because when you lose every little thing you may have, it's not easy to recover ... but we have not lost our faith."

White House: Puerto Rico response has been 'phenomenal'

Until Monday night, Trump hadn't tweeted or made public remarks on the shattered island for several days

He began his tweets with references to Texas and Florida, where Hurricanes Harvey and Irma struck recently.

"Texas & Florida are doing great but Puerto Rico, which was already suffering from broken infrastructure & massive debt, is in deep trouble.."

Texas & Florida are doing great but Puerto Rico, which was already suffering from broken infrastructure & massive debt, is in deep trouble.. — Donald J. Trump (@realDonaldTrump) September 26, 2017

"...It's old electrical grid, which was in terrible shape, was devastated. Much of the Island was destroyed, with billions of dollars...."

...It's old electrical grid, which was in terrible shape, was devastated. Much of the Island was destroyed, with billions of dollars.... — Donald J. Trump (@realDonaldTrump) September 26, 2017

"...owed to Wall Street and the banks which, sadly, must be dealt with. Food, water and medical are top priorities - and doing well. #FEMA"

...owed to Wall Street and the banks which, sadly, must be dealt with. Food, water and medical are top priorities - and doing well. #FEMA — Donald J. Trump (@realDonaldTrump) September 26, 2017

Asked about Trump's comments on Puerto Rico, Yulin, the San Juan mayor, said Tuesday that hurricane relief and the debt crisis are " two different issues.

JUST WATCHED San Juan Mayor: You don't put debt over people Replay More Videos ... MUST WATCH San Juan Mayor: You don't put debt over people 01:59

"You don't put debt above people -- you put people above debt. ... Let's deal with the two issues in a separate way, because there is a humanitarian crisis," she said.

Top aides to Trump, including homeland security adviser Tom Bossert and FEMA Administrator Brock Long, went to the island Monday to assess immediate needs.

"The response today has been phenomenal," acting Homeland Security Director Elaine Duke said Tuesday.

Long said the administration's objectives continue to be to "take care of people and stabilize the situation and do everything that we can to sustain life."

This heartbreaking message is from our flyover of #PuntaSantiago. #Humacao #PuertoRico needs a bigger response, & it needs it now. pic.twitter.com/8d7UH4vw7Q — NYU Primatology (@nyuprimatology) September 25, 2017

Amateur radio operators help out

Because the storm knocked out radio systems used by police and utility workers, amateur radio operators are helping them communicate with each other.

Oscar Resto is the American Radio Relay League's section manager in Puerto Rico. He and about 24 fellow members of the amateur radio group in Puerto Rico have been running police and utility radio operations since Maria hit.

Trained and licensed operators have been riding with police officers and utility workers with battery- or generator-powered kits.

And the American Radio Relay League is just getting started.

On the US mainland, CEO Tom Gallagher's phone lit up around 10 p.m. Friday. It was the Red Cross.

"We need 50 of your best radio operators to go down to Puerto Rico," Gallagher says a Red Cross representative told him.

Less than 48 hours later, 50 of them had signed up for a three-week deployment to Puerto Rico.

"Everything from rich guys to firefighters," Gallagher says.

Gallagher's team went to work with their manufacturers and dealer partners, scrambling to compile the self-sustaining kits the operators will need in Puerto Rico.

Long lines at San Juan airport

Hundreds of people have packed the main terminal at San Juan's Luis Muñoz Marín International Airport this week, hoping to escape the devastation -- but leaving hasn't been easy.

Because of damage to radar and other equipment at the airport, only about 10 commercial flights between San Juan and the US mainland could take off and land Monday -- and the same number is scheduled for Tuesday, airport authorities told CNNMoney

People are waiting in a main terminal that -- because it is running on limited emergency power -- has no air conditioning.

"Everyone is in the same boat, trying to get out," Leyla Colon, standing in line at the airport Monday, told Reuters. She said she couldn't buy tickets before she arrived at the airport, because she didn't have Internet or cellphone service.

"At this point I'll buy a ticket on any flight to get out of here," Colon told Reuters.

Stranded passengers rest Monday at San Juan's Luis Muñoz Marín International Airport.

Dozens more flights with relief material -- meals, water and generators -- have come into the airport, the Federal Aviation Administration said.

The first commercial flight from San Juan to New York's John F. Kennedy International Airport since Maria landed Monday night, to the relief of the 200 passengers' relatives.

Sarita Mongelli's parents, in their 80s, were on the flight.

"I can't describe the feeling after five days (of) not talking to them," Mongelli told CNN affiliate WABC . "I can't tell you what they've gone through -- horrible, horrible conditions -- and at this age, it's very hard for them."

Mongelli said her parents want to return to Puerto Rico but won't be going back anytime soon.

"Whatever's left of their life right now, they need to be safe with their children, not alone," she told the TV station. "We can't ask for more, I got them home -- I'm taking them home with me now."

'We're on a mission'

At Atlanta's international airport, aid workers were preparing Tuesday to board a charter flight to San Juan. Among them were 31 members of the New York City Fire Department, many of whom are of Puerto Rican descent.

"As Puerto Rican New York City firefighters with family that live in Puerto Rico, devastated by Hurricane Maria, we're on a mission to do what we can as best as we can, to get to all the people we can," said Lt. Joe Montalvo, a fireman from Battalion 57 in Brooklyn.

The firefighters loaded supplies onto the plane, including special cases of blood in refrigerated containers.

Montalvo said he had yet to speak with relatives living on the island.

"Phone service is still down, cellphone service is limited," Montalvo said. "My family (lives) in the southwest corner of the island, and we haven't heard anything from anybody."

He added, "We're hopeful they're OK."

CLARIFICATION: This story has been updated throughout to reflect the full last name of San Juan Mayor Carmen Yulín Cruz.