A federal jury in New York on Monday found the Palestinian Authority and the Palestine Liberation Organization liable for supporting six terrorist attacks in Israel more than a decade ago and ordered the groups to pay $218.5 million to the American victims’ families.

Monday’s verdict in Manhattan federal court follows a lengthy legal battle stemming from a lawsuit filed in 2004 under the U.S. Antiterrorism Act. The 1992 law, which allows U.S. victims of international terrorism to seek remedy in federal court, automatically...