The legislation would, among other things, amend a 1976 law that grants other countries broad immunity from American lawsuits — unless the country is on the State Department’s list of state sponsors of terrorism (Iran, Sudan and Syria) or is alleged to have committed a terrorist attack that killed Americans on United States soil. The new bill would clarify that foreign governments can be held liable for aiding terrorist groups, even if that conduct occurred overseas.

Advocates say the measure is narrowly drawn, but administration officials argue that it would apply much more broadly and result in retaliatory actions by other nations. The European Union has warned that if the bill becomes law, other countries could adopt similar legislation defining their own exemptions to sovereign immunity. Because no country is more engaged in the world than the United States — with military bases, drone operations, intelligence missions and training programs — the Obama administration fears that Americans could be subject to legal actions abroad.

The legislation is motivated by a belief among the 9/11 families that Saudi Arabia played a role in the attacks, because 15 of the 19 hijackers, who were members of Al Qaeda, were Saudis. But the independent American commission that investigated the attacks found no evidence that the Saudi government or senior Saudi officials financed the terrorists.

Proponents of the legislation cite two assassination cases in which legal claims were allowed against Chile and Taiwan. Administration officials, however, say that those cases alleged the direct involvement of foreign government agents operating in the United States.

The current debate is complicated by the fact that Saudi Arabia is a difficult ally, at odds with the United States over the Iran nuclear deal, a Saudi-led war in Yemen and the war in Syria. It is home of the fundamentalist strand of Islam known as Wahhabism, which has inspired many of the extremists the United States is trying to defeat. But it is also a partner in combating terrorism. The legislation could damage this fraught relationship. Riyadh has already threatened to withdraw billions of dollars in American-based assets to protect them from court action.