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WASHINGTON — The Supreme Court ruled Tuesday that thousands of victims of terrorist attacks overseas cannot sue a foreign bank under a U.S. law dating from the 1700s.

By a 5-4 vote, the court refused to revive lawsuits, dismissed by the lower courts, that sought to hold Arab Bank, which is headquartered in Jordan, responsible for attacks against foreign nationals in the Middle East. More than 6,000 survivors and relatives of those killed in the West Bank and Gaza claimed that officials of the bank were complicit in the attacks.

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Beginning in 2004, the victims filed a series of lawsuits accusing the bank of helping to finance Hamas and other terror organizations. The legal action was filed in the U.S. and aimed at Arab Bank through its branch in New York. The lead plaintiff in the case before the Supreme Court, Joseph Jesner, lost his 19-year-old son to a suicide bombing in Tel Aviv.

The lawsuits invoked one of the first laws ever passed by Congress, the Alien Tort Statute of 1789, known as ATS, intended to be a forum for resolving claims of piracy. But Tuesday's ruling said the law did not allow lawsuits of the kind filed by the terror victims.

"Absent further action from Congress, it would be inappropriate for courts to extend ATS liability to foreign corporations," wrote Justice Anthony Kennedy for the court's majority.

"Courts are not well suited to make the required policy judgments that are implicated by corporate liability in cases like this one."

In a separate concurring opinion, Justice Samuel Alito said allowing such lawsuits "would precipitate exactly the sort of diplomatic strife that the law was enacted to prevent."

But Justice Sonia Sotomayor, writing for herself and Justices Ruth Bader Ginsburg, Stephen Breyer, and Elena Kagan, said Tuesday's decision "absolves corporations from responsibility under the ATS for conscience-shocking behavior."

The ruling does not affect a separate lawsuit bought by U.S. victims accusing Arab Bank of helping to facilitate terrorist attacks in Israel. That claim was filed under a separate law.