“What this has done is it’s made the effects of American law felt in far-off places, and that is significant,” said Jonathan Schanzer, vice president for research at the Foundation for Defense of Democracies and a former terrorism finance analyst for the Treasury Department. “I don’t think any country, any bank, would want to be cut off from the U.S. financial sector, and they’re going to start thinking very carefully about whether they accept financial transactions” even from people or groups who are not on designated terrorist lists.

Shand S. Stephens, a lawyer for Arab Bank, said he was confident that the Second Circuit Court of Appeals was “going to reverse” the jury’s decision.

The case focused on transactions Arab Bank handled during the second Palestinian uprising. The plaintiffs accused Arab Bank of handling transactions for a number of well-known terrorists, and helping to route transactions for a charity called the Saudi Committee. That charity, the plaintiffs argued, sent payments to the families of Hamas suicide bombers, pointing to a Saudi Committee spreadsheet that included the names of relatives of some of those bombers.

Arab Bank holds that of all the accounts and transactions it processed in that period, only a few are in question, along with the large number of payments it processed for the Saudi Committee. It said the Saudi Committee is a legitimate charity that was never listed as a terrorist organization by the United States. And it said it properly checked all accounts and transactions against the appropriate blacklists, and any transactions that did go through were because of errors, such as different renderings of names in Arabic and in English.

Even if the terrorists were not on the relevant blacklists, the plaintiffs argued, Arab Bank employees should have known that the people were terrorists.

Mr. Stephens countered that designating terrorists is the government’s job. “The proposition that’s being floated here,” he told the jury, is “that private businesses, including banks, are supposed to make up their own lists of terrorists. Imagine, actually, what that would do, if a bank did that.”

The jury, which returned a verdict after two days of deliberations, was apparently unpersuaded. One juror who agreed to speak to the news media, Jill Rath, echoed the plaintiffs’ arguments, saying that “the money and the financing is the oxygen for the terrorists.”