WASHINGTON—A measure introduced in the House of Representatives that would require asbestos trusts to make regular quarterly reports about claims and other activities to bankruptcy courts is winning praise from the insurance industry and others.

Supporters of the bill—the Furthering Asbestos Claims Transparency Act of 2012, or H.R. 4369—argue that it is necessary to get compensation to those who are truly sick and to prevent fraud. But opponents say the measure is unnecessary.

The bipartisan measure was introduced this month by Reps. Ben Quayle, R-Ariz.; Jim Matheson, D-Utah; and Dennis Ross, R-Fla.

“This legislation will provide sunshine and transparency to the asbestos trust system,” Rep. Quayle said in a statement issued upon the bill's introduction. “The opaque and unsupervised way in which the system operates leaves it wide open to fraud and abuse, which endangers the very existence of asbestos trusts.”

“There's increasing concern about the asbestos trusts,” said Melissa Shelk, vp of federal affairs at the American Insurance Assn. in Washington. Ms. Shelk noted that more than 50 trusts are in operation, but there is no clearinghouse to determine who is receiving benefits.

The trusts are personal injury settlement funds created through the bankruptcy process, said Harold Kim, executive vp at the U.S. Chamber Institute for Legal Reform in Washington. The 60 trusts represent the assets and liabilities of the major asbestos defendants driven into bankruptcy. Mr. Kim said the trusts had accumulated more than $36 billion in assets as of last year.

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“One of the more significant problems is the fact these trusts do not link payments across themselves,” he said. “They're all very separate and independent,” with no centralized way to determine the legitimacy or veracity of a claim, he said.

In addition, there's no linkage between the bankruptcy trusts and the tort system, where current solvent defendants are sued, he said. Thus, there's no transparency about what they are filing and saying in the two systems, and there is no “orderly way for defendants in the tort system” to access filings in the trusts, said Mr. Kim.

Meanwhile, solvent defendants in the tort system are facing increased liabilities, he said.

Ms. Shelk said the proposed legislation is important for several reasons. “We don't know who is getting payments out of any trust,” she said. “There's no public information out there. You don't know if people are being paid out of multiple trusts for the same injury.”

“The issue is to bring transparency on who is getting paid, what they're getting paid, and what the allegations are they're making to get the money,” she said.”The trusts need to be there for people who are really sick.”

“The bill would help ferret out fraud in asbestos litigation by giving defendants a tool to verify that claimants are providing reliable and consistent exposure history information on bankruptcy trust claim forms and in civil litigation,” said Mark A. Behrens, a partner in the Washington office of Kansas City. Mo.-based law firm Shook Hardy & Bacon L.L.P. “This would help future claimants by preventing trust and defendant assets from being drained by false or exaggerated claims.”

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Mr. Behrens said the “modest and targeted” bill is designed to “address a major issue in asbestos litigation today: the need for greater transparency between the trust and tort systems.”

Ms. Shelk said that while there have been some efforts at the state level to bring more transparency to the trusts' operation, the House bill “is the first step in moving the legislation at the federal level.”

But there is disagreement over whether the system needs reform.

“I don't think there is any problem,” said Charles S. Siegel, a partner in the Dallas law firm Waters & Kraus L.L.P.

“The acid test of whether there is a problem is the results of trials,” said Mr. Kraus, who has represented plaintiffs in asbestos liability cases. “The theory behind these bills is that somehow tort defendants are being denied evidence of other exposures to products made by the bankrupt companies. I don't agree at all with the premise of these bills that tort defendants cannot get the discovery they need.”

“This bill shields asbestos manufacturers and insurers from accountability by delaying justice for Americans suffering from asbestos-related diseases,” Gary M. Paul, president of the American Assn. for Justice, said in an email. “Congress should instead focus on protecting victims of asbestos exposure and looking into why this deadly product is still in use in the U.S.”

But the bill's chances in the current Congress appear slim. “Until after the elections, any legislation that has well-funded opposition is going to have difficulty gaining momentum even though it is totally fair and much needed,” said a Capital Hill veteran.