Congress cleared a bill Friday that would allow family members of victims of the Sept. 11 terrorist attacks to sue the government of Saudi Arabia, setting up a potential clash with the White House, which has suggested it could veto the measure.

The Obama administration opposes the bill, known as the Justice Against Sponsors of Terrorism Act, over concerns that it could harm relations with Saudi Arabia, a key counterterrorism partner. Administration officials also have warned the legislation could weaken the global norm of sovereign immunity and encourage other countries to allow lawsuits by their citizens against the United States and its allies.

House lawmakers passed the bill by a voice vote under suspension of the rules, about an hour after a solemn ceremony on the Capitol steps to remember the 9/11 attacks. The ease with which it cleared the House, combined with the bill’s unanimous passage in the Senate in May, suggests that a presidential veto would likely be overturned.

“If any foreign government, if it can be shown to have supported a terrorist attack on U.S. soil, American victims ought to have the right to sue that country,” Rep. Ted Poe, R-Texas, a senior member of the House Foreign Affairs and Judiciary committees, said on the floor Friday. “It’s interesting that Saudi Arabia objects to this legislation. Methinks they object too much.”

The legislation would narrow the immunity that foreign states and their employees now enjoy from being sued in U.S. courts by giving district courts the jurisdiction to hear cases related to attacks carried out by designated terrorist organizations on U.S. soil with suspected support from other nations.

The Saudi government strongly opposes the legislation. It is eager, experts say, to avoid embarrassing lawsuits in U.S. courts that could put a spotlight on Riyadh’s perceived negligence in combating terrorist financing by Saudi citizens in the years and months before the Sept. 11 attacks, even if potential legal claims fail to prove the royal family’s outright complicity in the attacks.

 John T. Bennett contributed to this report.