Trump also announced that he would visit Puerto Rico next Tuesday, saying it was the earliest he could reach the battered island.
"Thank you to Carmen Yulín Cruz, the Mayor of San Juan, for your kind words on FEMA etc. We are working hard. Much food and water there/on way," he wrote on Twitter Tuesday morning, moments after Yulín Cruz appeared on CNN's "New Day."
Sharing harrowing details of rescue efforts in her city, Yulín Cruz praised the Federal Emergency Management Agency's "great job" and "logistics help."
"Our bodies are so tired, but our souls are so full of strength that we will get to everyone we can get to," she said.
Maria made landfall on Puerto Rico last week, whipping the island
with Irma-level winds, drenching it in Harvey-level flooding, crippling communications, decimating buildings and damaging a dam that puts downstream residents at risk of catastrophe. Without power and communications for much of the island, millions of people have been cut off from the world since the hurricane hit.
After days of public silence on the hurricane, Trump tweeted criticism Monday evening, casting blame on the island's poor infrastructure and economic instability.
"Texas & Florida are doing great but Puerto Rico, which was already suffering from broken infrastructure & massive debt, is in deep trouble. It's old electrical grid, which was in terrible shape, was devastated. Much of the Island was destroyed, with billions of dollars owed to Wall Street and the banks which, sadly, must be dealt with. Food, water and medical are top priorities - and doing well. #FEMA," he wrote in a series of tweets.
Responding Tuesday, Yulín Cruz said, "These are two different topics. One topic is the massive debt, which we know we have and it's been dealt with. But you don't put debt above people, you put people above debt."
Trump traveled to Texas and Florida in the immediate aftermath of the major storms that struck them earlier this month, but officials said Monday the devastated territory was not yet capable of hosting a presidential visit. In announcing his upcoming visit on Tuesday, Trump said he may also stop in the US Virgin Islands.
Asked about a potential visit from the President, Yulín Cruz defended Trump and emphasized the need for federal funding.
"I am sure that as the United States President, you know, he can come to Puerto Rico if he wants to. He has been not only tweeting, but I know he has been in contact with the governor, and we appreciate that. Let's make sure that this is not a handout, this is a moral imperative, and it is a plea for help and it a plea for us to be done right," she said.
The President is scheduled to receive a briefing on hurricane recovery efforts from homeland security adviser Tom Bossert later Tuesday morning. Bossert traveled to Puerto Rico alongside FEMA Administrator Brock Long on Monday to assess damage and federal needs.
The administration has not yet sent a disaster spending request to Congress, and it's not clear whether Bossert will have a fixed dollar amount to present to the President during his Tuesday briefing.
As of Monday morning, FEMA had $5.03 billion available for disaster spending between now and the end of September, an agency spokesperson told CNN. When the new federal fiscal year begins on October 1, the disaster relief fund will be replenished with an additional $6.7 billion.
Two senior House GOP sources tell CNN they expect to get the official request from the Trump administration in mid-October. A senior administration official says that is the White House's expected timing as well.
Defending the federal response in Puerto Rico as "anything but slow" Monday, White House press secretary Sarah Sanders said the administration will be able to determine appropriate funds "once we have a greater insight into the full assessment of damage."
Trump's relatively muted reaction to Maria -- he tweeted frequently over the weekend on myriad other topics, most notably his ongoing feud with the NFL
-- has drawn comparisons to his responses to Hurricanes Harvey and Irma, which primarily battered Texas and Florida, respectively.
As those hurricanes hit the states, Trump often tweeted comments on the size and impact of the storm as well as praising first-responders.
Before his latest messages this week, Trump last tweeted about Maria on Wednesday, the day it made landfall in Puerto Rico. The next day, he mentioned the situation to reporters while taking a photo with the Ukrainian president, saying the island was in "very, very, very tough shape" adding that its electrical grid was "destroyed."
But he didn't make any public comments about the island over the weekend.
Some Democrats worry that Puerto Rico is not getting the same amount of swift attention that Florida and Texas received.
"The fact of the matter is the administration has not been able to comprehend the fact that people in Puerto Rico are dealing with life and death issues," Rep. Nydia Velazquez, D-New York, the first Puerto Rican woman elected to the House, told CNN's Kate Bolduan Tuesday morning.
"The most fundamental duty of the President of the United States is to protect the homeland," she added.
In response to Democrats' concerns, Rep. Rodney Frelinghuysen, who chairs the House appropriations committee that is working on an aid package, said the island's residents will get the same help as those in the mainland US.
"The people of Puerto Rico and the US Virgin Islands remain in our thoughts as they struggle to recover from successive Hurricanes Irma and Maria. The challenges they face are truly tremendous. But they should be reassured that they are entitled to equal treatment under the law and the Appropriations Committee and House leadership will assure that every step of the way," he said.