Torture victims faced skepticism on Tuesday at the Supreme Court, where justices questioned whether foreign organizations, including oil titan Royal Dutch Shell PLC and the Palestinian Authority, could be sued in U.S. courts for violating international law.

The Alien Tort Statute, adopted by the First Congress in 1789, permits foreigners to sue in federal court for violations of treaties or the "law of nations," which today is understood to prohibit torture, genocide and crimes against humanity. More than two centuries later, President George H.W. Bush signed the Torture Victim Protection Act, authorizing U.S. citizens and aliens alike to sue perpetrators of torture and "extrajudicial killing" overseas.

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Shell's attorney, Kathleen Sullivan, a corporate litigator and Stanford professor, argued the opposite side of that coin. No international-law precedents authorize corporate liability, either, she said.

In the second case, Mr. Mohamad's lawyer, Stanford Prof. Jeffrey Fisher, tried to persuade the justices that references to "individual liability" in the Torture Victim Protection Act also covered actions by such organizations as the Palestinian Authority.