The chairman of crucial U.S. House subcommittee said a bipartisan bill of its own that will renew the Terrorism Risk Insurance Act, or TRIA, will be unveiled in June.

Rep. Randy Neugebauer, R-Texas, disclosed as much on May 20, in his capacity as chairman of the Subcommittee on Housing and Insurance of the Committee on Financial Services. His comments were brief, but came at the start of a hearing scheduled to consider a number of other bills that would reform various aspects of domestic insurance policy and regulation.

“Just to let you know, we are very hard working on this issue,” Neugebauer said at the start of the hearing, which Congress broadcast on the web. “Our goal is sometime in June to put out a bipartisan bill on TRIA, out of this committee, and put it in the hands of the leadership and look at passing it on the House Floor.”

Neugebauer cautioned that “it doesn’t always go on schedule,” but added “that is the schedule we have today.” He also did not disclose details of what a bipartisan TRIA bill from the House would include or leave out.

Even so, Neugebauer’s comments suggest that the push for TRIA renewal is beginning to gain some steam. Until now, the House has dealt with at least three pending TRIA renewal bills that didn’t have much traction. In April, a bipartisan bill emerged from the U.S. Senate that would, in part, institute small increases in insurer copays and other measures to tweak the net cost to the U.S. government.

The post-9/11 law, renewed twice previously, is set to expire again on Dec. 31, 2014. TRIA would provide federal reinsurance coverage in the wake of a terrorist attack, and has support of the insurance industry and many in the business community. Some Republicans and other groups, such as the Consumer Federation of America, are pushing to let TRIA lapse or make major changes because they see it as hampering a viable private terrorism insurance market.