The owners of hedge fund-backed reinsurers, including one tied to John Paulson, could have to pay more taxes or shift their focus under a bill introduced by Senator Ron Wyden to counter what he called abuses by offshore companies.

“For over 10 years now this loophole has allowed some hedge fund investors to avoid paying hundreds of millions of tax dollars,” Wyden, the top Democrat on the Senate Finance Committee, said in a statement Thursday. “It’s time we shut it down for good.”

Hedge fund managers can lower the rate they pay on profits and postpone the bills indefinitely by routing investments through reinsurers in offshore locations like Bermuda. David Einhorn and Dan Loeb are among hedge fund managers who set up reinsurers outside the U.S., and the companies have said they are legitimate businesses taking on risks from primary insurers and not tax dodges.

Under the Oregon senator’s bill, a company couldn’t qualify as an insurer for tax purposes if insurance liabilities are less than 10 percent of assets. When the ratio is 10-25 percent, the determination would be based on “facts and circumstances,” according to an overview of the bill.

“Legitimate insurance companies will be able to meet the 25 percent test,” according to the overview.

PacRe Ltd., a reinsurer set up by Paulson, had a ratio of about 1 percent at the end of 2012, according to a report by the Joint Committee on Taxation on Bermuda-based insurers in 2013. Loeb’s Third Point Reinsurance Ltd. had a ratio of 11.9 percent.

The Internal Revenue Service, in proposed rules published in April, said favorable treatment shouldn’t apply to companies that borrow insurance executives from another firm. Paulson’s PacRe has relied on Bermuda-based Validus Holdings Ltd. for underwriting staff.

Manoj Gupta, who handles investor relations at Third Point Re, didn’t immediately return a message seeking comment, nor did spokespeople for Paulson and Validus.

While Wyden has long been pushing for tighter rules on hedge fund reinsurers, the issue has drawn less attention from Republicans, who hold the Senate majority.