The head of the Federal Emergency Management Agency’s urban search and rescue unit has resigned, telling colleagues he was frustrated by bureaucratic hurdles the Trump administration imposed that delayed the agency’s response to deadly flooding in Texas, according to three people familiar with his reasoning.

Ken Pagurek, who worked with FEMA’s search and rescue branch for more than a decade and served as chief for the past year, told associates that his concerns had been mounting since the start of hurricane season and that the administration’s changes to the agency were causing “chaos.”

He said he worried that a new policy that requires purchases of more than $100,000 be personally approved by Kristi Noem, the homeland security secretary, could hurt disaster response efforts that require speed and agility.

Experts have said that responses during a disaster can quickly total billions of dollars, and that requiring personal approvals for expenses of $100,000 and above could easily create bottlenecks.

“This decision was not made lightly, and after much reflection and prayer, it is the right path for me at this time,” Mr. Pagurek wrote in a resignation letter. His departure was first reported by CNN.

Mr. Pagurek could not be reached for comment.