"My argument to him was, I have some ideas, but there are people who have even more, better ones, because they live or lived in Puerto Rico, they understand its politics, its economics, its pre-existing challenges and its long-term opportunities", he said.
Perry said that Trump most likely meant that FEMA has a "finite mission and a finite amount of time".
Puerto Rico has been grappling with a bankruptcy crisis and owes $72 billion to creditors. The death toll in Florida after Hurricane Irma, which made landfall on September 10, also reached 75, the Miami Herald reported, not counting the more than 38 people who died in the Caribbean.
"Congress to decide how much to spend.We can not keep FEMA, the Military & the First Responders, who have been wonderful (under the most hard circumstances) in P.R. forever!" he added.
The Federal Emergency Management Agency can (and does) stay involved in disaster relief for years after major catastrophes.
Trump criticized the US territory in a series of tweets Thursday. House Speaker Paul Ryan, R-Wis., said the government needs to ensure that Puerto Rico can "begin to stand on its own two feet" and said the USA has "got to do more to help Puerto Rico rebuild its own economy".
Some conservatives displayed early signs of spending fatigue.
White House legislative affairs director Marc Short said on CNN's "The Situation Room" that he did not view Trump's tweets as a "threat" to withdraw aid to Puerto Rico and conceded he did not know why Trump chose to make those statements Thursday morning.
"There is some concern about can we couple some of this (disaster aid) with reform measures", Cole told Reuters on Wednesday.
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Vox reported that conflicting numbers from the USA government and the Puerto Rican government have made it hard to estimate exactly how many people died - a figure that could go well into the hundreds.
Cole said the price tag could rise as relief efforts transition from emergency response to rebuilding.
Trump's remarks on Thursday cap those he said while visiting the island on October 3 when he said Puerto Rico's hurricane wasn't a "real catastrophe" like Hurricane Katrina and that response to relief efforts were "throwing our budget a little out of whack".
"They're basically three weeks now living in the 19th century", Rubio said.
White House Chief of Staff John Kelly told reporters the Trump administration would "stand with those American citizens in Puerto Rico until the job is done".
On top of that, the death toll is expected to be higher than originally believed.
Both Trump and Vice President Mike Pence visited the island last week to reaffirm the USA commitment to the island's recovery.
The House bill would provide $18.7 billion for FEMA's disaster-relief fund, $16 billion to replenish the nation's flood-insurance program and $576.5 million for wildfire efforts.
Rubio said it is up to the oversight board charged with resolving Puerto Rico's debt crisis to determine how to address the island's debt, noting that private debt owed to investors with legal recourse can not simply be "forgiven" by the federal government.