WASHINGTON — Democrats and Republicans are vowing to decisively override President Barack Obama’s veto of a bill to allow families of Sept. 11 victims to sue the government of Saudi Arabia for the kingdom’s alleged backing of the terrorists who killed nearly 3,000 people.

Obama rejected the bill Friday, warning of a host of unintended and severe consequences if it were enacted. The legislation, according to Obama, could leave American troops and diplomats overseas vulnerable to lawsuits in foreign courts from people seeking redress for actions taken by armed groups that are backed or trained by the United States.

The bill’s proponents disputed Obama’s rationale, arguing the measure is narrowly tailored and applies only to acts of terrorism that occur on U.S. soil.

“This is a disappointing decision that will be swiftly and soundly overturned in Congress,” said Sen. Chuck Schumer, D-N.Y., who sponsored the bill. “If the Saudis did nothing wrong, they should not fear this legislation. If they were culpable in 9-11, they should be held accountable.”

Sen. John Cornyn, R-Texas, another of the bill’s sponsor, criticized Obama for failing to listen to the families of the victims and said he looked forward to the opportunity for Congress to override the veto.

The bill, which has strained already tense relations with a key Middle East ally, passed the House by voice vote earlier this month. The measure cleared the Senate in May, also by voice vote.

Saudi Foreign Minister Adel bin Ahmed Al-Jubeir had warned lawmakers they were on a path to turning “the world for international law into the law of the jungle.”

Saudi Arabia had no immediate comment Friday on the veto, which came two days after the Senate voted convincingly to back a $1.15 billion sale of American weapons to the kingdom.

The legislation gives victims’ families the right to sue in U.S. court for any role that elements of the Saudi government may have played in the 2001 attacks that killed thousands in New York, the Washington, D.C., area and Pennsylvania.