Mr. Berkley reported that a foreign competitor that wrote a similar amount of U.S. commercial business last year paid only $19 million in taxes, while W.R. Berkley paid $260 million. "That's a significant competitive advantage," he said.

He also said that making his case that foreign counterparts should pay comparable tax amounts won't be a hard one to sell in Washington. Seemingly outlining his pitch to federal lawmakers, he said that companies in Bermuda and other offshore locations can outsource their processing jobs to places like India, leaving no business here beyond shell companies collecting U.S. dollars.

At a later session, Edward Noonan, chairman of Bermuda-based Validus Reinsurance, responded, saying that "Bermuda plays a vital role in financing American risk competitors" and that Bermuda has its own local tax regime.

Changing tax rules to create a more level playing field, he said, would "only increase the cost of risk to the United States," adding that U.S. companies "would be hard-pressed to deliver Bermuda capacity."

John Charman, CEO of Axis Capital, said, "We are where the capital wants us to be."

During the opening session, Mr. Berkley, when asked to identify the most worrisome risk facing insurers, focused not on tax issues but on the potentially temporary nature of capital coming in from reinsurance sidecars being set up in Bermuda, and other financial arrangements that are not classic insurance.

Noting that some companies are "betting their survival" on new vehicles backed by lengthy contracts, Mr. Berkley asked, "How will those 65-70 page documents play out if something goes wrong?"

Joseph Brown, non-executive chairman of Seattle-based Safeco and executive chair of Armonk, N.Y.-based MBIA, countered that the new vehicles have some positive consequences.

"They are bringing capital market efficiencies to other players in the market," he said. "You don't have to use them directly for them to have an effect," he said, suggesting, for example, that their existence eats into the profits of some reinsurance behemoths like Berkshire's National Indemnity, led by Ajit Jain.

"It keeps Ajit's returns from being this big to this big," he said, gesturing to make his point that the vehicles are "keeping the market honest in terms of capital returns."

While Mr. Brown noted the ability of capital to move in at an accelerated pace--potentially shortening the length of the insurance cycle--Mr. Berkley posed questions about how quickly it will move out. "What happens when the first event happens and you've used up your financial transaction, and those players don't want to come back in? A second event happens and you're naked," he said.