Puerto Rico, a U.S. territory, was hit by Hurricane Maria in September 2017, causing some $100 billion in damage.
The HUD inspector general does not have the power to investigate the White House; it is limited to reviewing the agency’s own staff, programs and policies. But any matters uncovered in the probe beyond its jurisdiction could be referred elsewhere.
“We’re in the process of looking into whether or not there has been any interference and do plan to report back to Congress on what we find,” Kirkland told the House Financial Services Committee.
Kirkland noted that the jurisdiction limitations in his testimony Tuesday.
“Where we can, we have asked those questions” about interference, he said.
Trump has accused local leaders in Puerto Rico of mismanaging funds, an allegation they deny. At a private lunch with Senate Republicans on Tuesday, the president carried with him spending charts to show lawmakers how much disaster aid other states have received in comparison. The Senate is considering a disaster relief funding bill.
White House spokesman Judd Deere said the island has already received "unprecedented support" and is "on pace to receive tens of billions of dollars" in federal money.
"However, the Trump Administration will not put taxpayers on the hook to correct a decades-old spending crisis that has left the island with deep-rooted economic problems,” said Deere.
Puerto Rico Gov. Ricardo Rossello has asked to meet personally with Trump, but said in a statement Tuesday he has yet to receive a confirmation.
"The comments attributed to Donald Trump today by senators from his own party are below the dignity of a sitting President of the United States," Rossello said. "They continue to lack empathy, are irresponsible, regrettable and, above all, unjustified."
He added, "I want to be very clear: Not a single federal dollar has been used to make debt payments. This has been the most transparent recovery in the history of the United States, providing unprecedented access and collaboration with federal agencies."
Rossello said he "can only assume" the bad information was from White House staffers and said to "stop listening to ignorant and completely wrong advice."
Last fall, Trump tweeted that Puerto Rico was using disaster relief “to pay off other obligations.”
“The U.S. will not bail out long outstanding & unpaid obligations with hurricane relief money!” he wrote.
Democratic Reps. Nydia M. Velázquez, of New York, Bennie Thompson, of Mississippi, and Raul Grijalva, of Arizona, pushed for the internal investigation in a letter to the inspector general last January. According to the letter, HUD allocated $20 billion in disaster recovery grants.
But despite agency approval, “we understand that HUD has yet to make little of these funds available," the lawmakers said.
HUD Secretary Ben Carson announced March 1 that the agency had approved a plan to distribute aid to Puerto Rico but with "tight fiscal controls" because of Puerto Rico's "history of fiscal malfeasance."
ABC News' Meridith McGraw, Joshua Hoyos and Trish Turner contributed to this report.