WASHINGTON - A Senate-approved bill that would allow families of Sept. 11 victims to pursue their lawsuit against Saudi Arabia is on track for a showdown when it comes up in the House next month over the Obama administration’s opposition.

Lawmakers are being lobbied by the White House, Saudi Arabia and victims’ relatives on the bill and the drive to release 28 secret pages of the 9/11 Commission report on the Saudi involvement with terrorists who attacked the United States 15 years ago.

Backers of the bill, called the Justice Against Sponsors of Terrorism Act, said they’re confident the House will pass it, despite a presidential veto threat and Saudi Arabia’s warning that it might pull billions of dollars from the U.S. economy.

“I believe we can take the Senate bill without any change and pass it in the House,” said bill sponsor Rep. Peter King (R-Seaford), citing the Senate’s unanimous voice vote approval and bipartisan support in the House.

The bill would modify the Foreign Sovereign Immunity Act, which federal courts have cited in dismissing Saudi Arabia from the lawsuit. Under the bill, the pending lawsuit could go forward to determine the role of Saudi Arabia in 9/11 and to seek billions of dollars in damages.

President Barack Obama opposes the measure because he’s concerned it could make the United States vulnerable to lawsuits in other countries’ courts, said White House spokesman Josh Earnest.

King said he is pushing for a House vote on the measure by July 15, before Congress breaks from July 18 to Nov. 14 for the presidential nominating conventions and political campaigns.

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But King said the bill’s fate is largely up to House Speaker Paul Ryan (R-Wis.), who sets the House agenda. Last month Ryan said he wanted to make sure “we are not making mistakes” with the measure. His office did not respond to queries.

In response to those concerns, Rep. Steve Israel (D-Huntington), a co-sponsor, said, “I imagine there may be some additional tweaks.”

King said he would prefer no changes to the Senate bill, to avoid any delay in its final passage by both chambers.

The next step will be a hearing and vote on the bill in the House Judiciary Committee. A committee aide said it will be held in the near future. King said it’s likely to be in June.

Sen. Chuck Schumer (D-N.Y.), who sponsored the Senate version with Sen. John Cornyn (R-Texas), has worked with the House Judiciary chairman, Rep. Bob Goodlatte (R-Va.), to address his issues with the legislation, King and Israel said.

Terry Strada, who leads the advocacy group 9/11 Victims’ Families and Survivors United for Justice Against Terrorism, said that she will return to Washington this week to lobby a dozen House members to vote for the Senate version of the bill.

Strada, a Westbury native who now lives in New Vernon, New Jersey, lost her husband, Tom, in the 9/11 attacks. He was among the hundreds of employees of the financial firm Cantor Fitzgerald who died when the terrorist-hijacked airliners hit the World Trade Center.

“We’re hoping there are no more changes in the bill. It really went through the grind in the Senate,” she said. “We did the best effort to address the concerns of the administration.”