Although the government has not requested the money, the company says it will "voluntarily" reimburse the costs associated with aid provided the Carnival Triumph in February and the Carnival Splendor in 2010, The Miami Herald reported Tuesday.
The company added "at no point in time has Carnival stated it would refuse to reimburse federal agencies if they sought remuneration."
The exact amount of the payment has not been determined, a spokesman said.
Fires aboard the ships knocked out power to the vessels. The U.S. Coast Guard escorted the ships back to land, and the U.S. Navy delivered tons of food to the Splendor.
U.S. Sen. Jay Rockefeller, D-W.Va., has estimated the costs at a combined total of $4.2 million.
"These costs ultimately must be borne by federal taxpayers," Rockefeller said in a March 14 letter to Carnival after the Triumph accident. "Given that you reportedly pay little or nothing in federal taxes, do you intend to reimburse the Coast Guard and the Navy for the cost of responding to either?"
In a reply to Rockefeller, Capt. James Hunn, a senior vice president for Carnival, did not refuse to reimburse the costs, but neither did he say the company would pay.
"Carnival's policy is to honor maritime tradition that holds that the duty to render assistance at sea to those in need is a universal obligation of the entire maritime community," he said.
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