Regulators in Florida "are going to have to think long and hard about the market they've created," Mr. McGavick said. "Air conditioning made Florida possible. The lack of insurance could bring it to a grinding halt," he said, repeating a warning he said he had once given to Gov. Jeb Bush.

"We had a rate [level] that we thought we could charge–reasonable, not crazy. There was a discomfort with that rate…And we have chosen to exit the state," he said.

Mr. Lilienthal, who attended a catastrophe insurance summit Wednesday in Burlingame, Calif., organized by California Insurance Commissioner John Garamendi, said that he had made the same point there.

He said his personal position, and that of CNA, is for strong support for quick renewal of the federal Terrorism Risk Insurance Act (TRIA) that supports terrorism insurance. But, he added, "We do not feel there is a need to put up a national disaster fund."

There's no ability to model terrorism, or to assess the average annual return periods of a terror event, he said, contrasting natural catastrophes. "There's a certain degree of predictability to that," he said.

"The biggest catastrophe would be to have the federal government involved," Mr. Kelly stated, drawing an analogy to the federal flood program. "It was originally set up to help poorer people," but within a few years, "it's become a way for the middle class and affluent to build homes on the outer banks."

Mr. McGavick said the private insurance mechanism has worked as expected in areas hard hit by storms. "Our people were on the front lines, ready to go in and help people, like they're supposed to. But the federal program…is a disaster," he said.

Mr. Kelly added: "Katrina was not a natural disaster. Katrina was a disaster of federal management of the levee system…It was a federal disaster caused by federal mismanagement."

Mr. McGavick said legal action brought by Mississippi Attorney General Jim Hood to force insurers to pay for storm surge hurricane damage, which carriers view as excluded flood coverage, created an obstacle to finding solutions.

"Unhelpful participants in the political process make it an unsafe environment for civil conversation about how to solve these problems," he said.

Because of that, according to Mr. McGavick, "the rest of us are constrained from having honest conversations that can help people and provide a private market as we would wish to do."

On TRIA, Mr. McGavick recounted the "strange conversations" that have taken place with senators who insist the free market can cover terror risk. "We are the free market," he said. "We'd love to make money at this. It is not insurable. We can't. Read our lips."

He added, "The idea that the federal government has no role in making up for the failure of its defenses makes no sense."

Mr. Lilienthal said there is not sufficient data to model terror risks. "If it comes out in color and its in Powerpoint and spread over a couple of pages," that doesn't mean you have good numbers for the amount of damage, lives lost and business interruption losses caused by a 10-pound bomb dropped on downtown Chicago.

The modelers can be wrong, and they've got more data. If he relies on such results and they prove to be wrong, "I've got a vaporized balance sheet. I'm done," he said.