US President Donald Trump has announced plans to travel to Puerto Rico as critics charge him with failing to respond adequately to the humanitarian crisis facing the island's 3.4 million residents.

"I grew up in New York, so I know many people from Puerto Rico," Trump told legislators on Tuesday. "I know many Puerto Ricans. And these are great people, and we have to help them. The island is devastated."

Also on Tuesday, at a joint news conference with Spanish Prime Minister Mariano Rajoy, the president described the government's relief efforts in Puerto Rico as "amazing," "tremendous," and "really good".

Trump's comments come amid intense criticism from both Republicans and Democrats.

Some residents in Puerto Rico have accused the Trump administration of being more sluggish in its response than it would to a disaster on the US mainland, even though Puerto Rico's inhabitants are US citizens.

The criticism was heightened by a series of Twitter messages by Trump on Monday about hurricane damage on Puerto Rico in which he also referred to the island's $72bn debt crisis and bankruptcy.

"Much of the Island has been destroyed, with billions of dollars owed to Wall Street and the banks which, sadly, must be dealt with," he tweeted.

Maria roared ashore Puerto Rico last Wednesday as the most powerful hurricane to strike the island in nearly a century, knocking out the territory's entire electrical grid, unleashing severe flooding and causing widespread heavy damage to homes and infrastructure.

The storm has claimed more than 30 lives across the Caribbean, including at least 16 in Puerto Rico.

'Unprecedented disaster'

It was the third major hurricane to hit the United States in less than a month, following Harvey in Texas and Irma in the Caribbean and Florida. Maria was downgraded to a tropical storm on Tuesday, far off the coast of North Carolina.

"We've gotten A-pluses on Texas and in Florida, and we will also on Puerto Rico," Trump told reporters in Washington. "The difference is this is an island sitting in the middle of an ocean. It's a big ocean; it's a very big ocean. And we're doing a really good job."

Trump visited Texas and Florida after Harvey and Irma. The last Republican president, George W Bush, faced widespread criticism for his administration's handling of Hurricane Katrina, which killed some 1,800 people in and around New Orleans in 2005.

Senate Democratic Leader Chuck Schumer said the island needed 1,000 to 1,500 additional security personnel and at least another 200 generators, as well as fuel for them. He urged Trump to propose an aid package to Congress in the next day or two.

READ MORE: Devastated scenes after Hurricane Maria

"With all due respect, President Trump, relief efforts are not 'doing well'," Schumer said.

But Puerto Rico Governor Ricardo Rossello, characterising Hurricane Maria as an "unprecedented disaster" for the island, said he was satisfied with the administration's relief efforts and called Trump's performance "excellent".

"They have responded very quickly," he told Reuters news agency by telephone, adding that he has spoken often with the president since the storm hit. He cited swift disaster declarations issued by Trump and a six-month waiver of FEMA's cost-sharing requirements.

"He has been very much concerned with the situation in Puerto Rico," Rossello said of Trump. "But they're conscious we still need more resources to the island."

US disaster-relief spending sufficient to last through mid-October has already been appropriated, White House budget chief Mick Mulvaney said.

"We are picking up most of the cost right now in Puerto Rico," he told reporters in Cleveland. "We are not penny-pinching in any fashion. We are taking care of folks."

The administration has about $5bn remaining in a disaster relief fund, and Congress has already approved another $7bn in funding that will become available on October 1, according to a House Appropriations Committee aide.

No electricity or fuel

Six days after the storm hit, much of the island remains inaccessible, communication is difficult and fuel is in short supply.

About 44 percent of Puerto Rico's population currently lacks access to clean drinking water, and the majority of the island's 69 hospitals are without electricity or fuel needed for generators, the US' defence department said.

FEMA has opened distribution centres in 16 cities in Puerto Rico and at 12 locations in the Virgin Islands to provide food, water and other commodities, the agency said, though many residents were struggling to get basic essentials.

"We've not seen any help. Nobody's been out asking what we need or that kind of thing," said Maria Gonzalez, 74, in the Santurce district of San Juan.

READ MORE: Hurricane Maria devastates Puerto Rico's capital

Help appeared to be reaching parts of the city, she said, pointing to Condado, a tourist area powered by generators while other San Juan streets fall into darkness at dusk.

"There's plenty of electricity over there, but there's nothing in the poor areas," Gonzalez said.

San Juan Mayor Carmen Yulin Cruz criticised Trump for focusing on the island's financial woes in his tweets.

"You don't put debt above people; you put people above debt," she told CNN.

Officials were still taking stock of what was expected to be a months-long effort to rebuild the island's power system, and many residents seemed resigned to a long wait for basic services to return. But few doubted the US government had the ability to bring the island back to its feet quickly.

"If they wanted to fix things fast, they could do it," said Carlos Arias, 41, as he waited in a line of people snaking around a block in San Juan to fill up a canister with petrol. "It's a question of will."