WASHINGTON – The chief of the federal disaster relief agency on Wednesday defended his office’s response to victims of Florida’s hurricanes against allegations of fraud and overpayments.

An audit showed that thousands of people who did not need aid cashed checks that totaled more than $31 million.

The allegations were based on “marginal cases” and did not reflect the typical response to disasters by the Federal Emergency Management Agency, Michael D. Brown told a Senate committee.

But an internal investigation by the Homeland Security Department, of which FEMA is a part, found “programatic, systemwide weaknesses” in aid distribution.

In Miami-Dade County, far south of Hurricane Frances’ worst damage, people collected checks for $6,500 as reimbursement for cars worth much less and could not provide proof of damage, according to the report by Richard L. Skinner, acting inspector general at Homeland Security.

Some people who received temporary living expenses when their home was declared “unsafe” because of a $100 broken window actually stayed there and pocketed the money, he reported.

“They were not living in tents, not living in shelters,” Skinner said. “They were not experiencing widespread trauma.”

The head of the Senate Homeland Security and Governmental Affairs Committee said it was a “pay first, ask questions later approach.” Sen. Susan Collins, R-Maine, disagreed with Brown’s assertion that payouts could not be much more efficient.

Noting that the next hurricane season was nearing, she said, “This issue has ramifications that are relevant to future disaster relief efforts in all regions of our country.”

Brown said private insurers paid $60 million in property damage claims to Miami-Dade County, indicating the county did have hurricane damage. But Collins said the threshold for federal aid should be much higher, and she feared a public backlash the next time communities seek disaster help.

Congress began investigating at the request of Sen. Bill Nelson, D-Fla., whose office took complaints from legitimate victims who had not received full payment.

“Either there is a problem in the structure of FEMA, the Congress in its oversight capacity should address, or there is poor management, or there is both,” Nelson said.

The audit cited allegations that FEMA paid $720,000 to 228 applicants for personal property items based only on the applicants’ verbal descriptions.