Tears of relief as aid starts to reach remote parts of Puerto Rico

— -- President Donald Trump's impending visit to storm-ravaged Puerto Rico and his public criticism of the U.S. territory's most prominent mayor appear to be the last thing on many people's minds on the island.

The vast majority of households and businesses in Puerto Rico still had no electricity as of Saturday, 10 days after Hurricane Maria wrought destruction on the island.

But there is hope as aid begins to reach even some of the territory's remote regions.

ABC News traveled with Federal Emergency Management Agency (FEMA) officials to Puerto Rico, including to some areas that have been cut off from communication with the rest of the island since Maria hit.

In the mountainous town of Juncos, locals cried in relief after FEMA workers and volunteers arrived to begin inspecting homes for repair as well as to bring much-needed essentials, like water, food and gasoline.

A volunteer but also a victim

Janet Espada is a FEMA volunteer who lives in Juncos.

Hurricane-caused flooding destroyed much of what was in her home. Still, she counts herself lucky.

"Other people have lost everything, their entire house is gone," Espada told ABC News.

Hurricane Maria pummels Puerto Rico, Caribbean

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A car drives on a damaged road in the aftermath of Hurricane Maria in Humacao, Puerto Rico, Oct. 2, 2017.

Ricardo Arduengo/AFP/Getty Images

Espada is among the FEMA volunteers now fanning all over the island.

A NASA rocket scientist from California, a lawyer from New Jersey, and college students from San Juan who are acting as translators are among the volunteers spending their days in stifling conditions setting up registration sites to help residents file claims with FEMA to get their houses inspected and fixed.

So far the agency has counted 63,000 applications and covered $7 million worth of assistance so far.

"I got here Sept. 8," Debby Stevens of New Jersey said. "We came for [Hurricane] Irma and survived Maria."

Stevens acknowledged that aid for the devastated island of about 3.5 million U.S. citizens seemed slow in arriving.

But, she said, "We're doing the most we can."

In addition to the FEMA workers, the Department of Defense now has 6,000 staff on the island.

'Walking in is very emotional'

The residents of Juncos weren't the only ones overwhelmed with feelings when FEMA arrived.

The agency's press secretary, Paul McKellipps, felt the same way as residents rushed up to shake his hand and thank him.

"Walking in is very emotional," McKellips said through tears. "These people have gone through the perfect storm. They don't have electricity; they can't find their loved ones. Having them express the gratitude that they have ... is pretty humbling."

He's also upset at what he sees as finger-pointing in the wake of Hurricane Maria.

Puerto Rico's infrastructure and electrical grid were already in such poor condition that no planning could have helped the island be ready for the storm, he said.

"It's not enough; it's not fast enough. They know that. We know that. We're doing as much as we possibly can," McKellips said. "We still have search and rescue teams that are out there. We're still in the early stages of this."

Houses with roofs and doors blown off may take weeks to fix

Food and medical aid are coming through, including a barge carrying water and meals that arrived Saturday.

Two million liters of water have been delivered to the island while over 1 million have been handed out, FEMA officials confirmed.

The huge Navy hospital ship, the USNS Comfort, is headed for the island to service the most hard-hit areas.

But a FEMA backlog means a damage claim on a home that normally would get a response within a few days might have to wait for 30 days, a site manager in the southeast city of Maunabo told ABC News.

Trump tweeted that 'all buildings now inspected for safety'

Trump tweeted Saturday that all buildings in Puerto Rico have been inspected, a claim that the island's governor was unable to confirm.

"I'm not aware of any inspections," Gov. Ricardo Rossello said. "Of course there are areas of Puerto Rico that we haven't gotten any contact" with.

"Perhaps he was referring to a particular set of buildings I'm not sure what the context was," Rossello said of Trump's assertion.

'A state of disadavantage and inequality'

Rossello, in an emotional speech Sunday in San Juan, urged fellow U.S. citizens on the mainland to see responding to the crisis in the U.S. territory as a "moral imperative."

"I want you to reflect why Puerto Rico is in its current state of disadvantage and inequality," he said. "It's not something that happened a few months and a few weeks prior to the storm. It is a condition that has happened for more than a century in Puerto Rico."

"I invite you to reflect and consider that Puerto Rico has the highest per capita participation in our military and armed forces compared to all the states," the governor said. But, he said, "right now we have over 150,000 veterans here that don't get equal treatment because they live here on the island."

Rossello also recognized support from the president and some congressional representatives and governors.

"I know there is more that we need to do, but it is important we recognize that the president, state governments are pledging support," Rossello said.

"I'm here to tell you as the chief executive of Puerto Rico that they are."

ABC News' Joshua Hoyos, William Gretsky and Whitney Lloyd contributed to this report.