But Mr. Thornburgh said no foreign court should hear cases under the RICO statute, a 1970s law aimed at fighting organized crime that allows civil penalties for certain criminal acts. “Only U.S. courts can adjudicate RICO,” he said in an interview in Moscow.

Bank of New York Mellon also contends that the improper wire transfers did not amount to a precursor crime under RICO, and that Russia’s claim to damages was not supported by evidence.

The bank says the Basmany Court’s decision will never be upheld outside of Russia. The same court heard the politically tinged bankruptcy case against the Yukos oil company, which ended in dismantlement of the company and was criticized for what some saw as judicial irregularities.

Still, Mr. Dershowitz, arguing for the Russian customs agency, said the Bank of New York should observe the court’s ruling. “A great bank founded by Alexander Hamilton will not want to be perceived as running away from judgment,” he said. The plaintiffs are arguing that the widespread harm caused to Russian people by the collapse of the Russian ruble should be considered in the damage calculation.

In many other legal cases, officials in Russia and other countries have objected to applying American law to disputes outside of the United States.

The practice has drawn objections in several widely publicized cases, including Exxon Mobil’s dispute with Venezuela and Cuban exile suits against the island’s Communist government. In the Venezuela case, Exxon sued in United States, British and Dutch courts.

Courts around the world, however, routinely apply other countries’ laws in contract disputes.

Bruce Marks, a Philadelphia lawyer who filed RICO claims against an aluminum conglomerate controlled by the Russian billionaire Oleg V. Deripaska, testified in court Thursday for the customs agency. Mr. Marks said that the American racketeering law could be applied in a foreign court, though no foreign court had yet passed judgment on such a case.