Hunn noted that Carnival ships frequently render assistance at sea at their own cost, including 11 times within the past year.
"We remain deeply grateful for all of the services performed by the brave men and women of the U.S. Coast Guard and U.S. Navy," he said.
Rockefeller released a statement late last week blasting the company for its response.
"Carnival's response to my detailed inquiry is shameful," he said.
He said cruise passengers deserve better and he was "considering all options to hold the industry to higher passenger safety standards."
On Monday, the company released a statement saying it has decided to help cover the rescue costs.
"Carnival Corporation is in the process of voluntarily submitting payment to the U.S. Treasury Department to reimburse the federal government for costs related to the Carnival Triumph and Splendor incidents," the company said in a statement.
The company also maintained it never said it would refuse to reimburse federal agencies if they directly asked for reimbursement.
"Although no agencies have requested remuneration, the company has made the decision to voluntarily provide reimbursement to the federal government," the statement said.
While pleased with the company's decision, Rockefeller left the door open to future hearings and action related to the cruise industry.
"I am still committed to making sure the cruise industry as a whole pays its fair share in taxes, complies with strict safety standards, and holds the safety of its passengers above profits," he said.
Rockefeller already has proposed a repeal of tax provisions that allow cruise companies to keep ships registered in foreign ports, sheltering them from American corporate taxes.
He is also considering further hearings to examine the industry's compliance with safety, security and environmental standards and determine if those regulations sufficiently protect passengers and the environment.
Contact writer Jared Hunt at busin...@dailymail.com or 304-348-4836.