(Recasts first paragraph, adds quotes from Justices Roberts and Alito, background on dispute)
WASHINGTON, Oct 11 (Reuters) - Conservative U.S. Supreme Court justices on Wednesday signaled concern about allowing companies to be sued under American law for human rights abuses abroad in a case involving allegations that Arab Bank Plc helped finance militant attacks in Israel and the Palestinian territories.
Chief Justice John Roberts and Justice Samuel Alito, both conservatives, indicated that U.S. foreign policy tensions that could arise from such cases would be a reason to curb corporate liability.
Their remarks during an hour of arguments in the case raised the possibility that the court, with a 5-4 conservative majority, could rule in favor of the Jordan-based bank in the lawsuit seeking to hold it financially liable for the Islamist attacks.
The court's four liberals indicated that corporations should not be immune.
Even if the court rules in favor of the roughly 6,000 plaintiffs suing the bank, the lawsuit could still be dismissed on other grounds once it returns to lower courts.
The plaintiffs accused the bank of being the "paymaster" behind attacks including suicide bombings because of its role in processing certain financial transactions. The plaintiffs include relatives of non-U.S. citizens killed in attacks and survivors of the incidents.
"I'm concerned about the foreign entanglement issue," Roberts told the plaintiffs' lawyer, Jeffrey Fisher.
Allowing corporate liability could lead to a "problematic result" by increasing foreign policy frictions with other countries where accused companies are based or where militant attacks take place, Roberts added.
Alito also mentioned the possibility of "serious foreign policy" repercussions.
The plaintiffs asked the Supreme Court to overturn a 2015 New York federal appeals court ruling that Arab Bank could not be sued under a U.S. law called the Alien Tort Statute, which dates back to 1789, because it is a corporation.
The law has been used in recent years by human rights lawyers to seek damages against companies in U.S. courts for human rights violations abroad. The lead plaintiff in the Arab Bank case is Joseph Jesner, whose British citizen son was killed at age 19 in a 2002 suicide bombing of a bus in Tel Aviv.
The plaintiffs filed several lawsuits in Brooklyn federal court, claiming Arab Bank used its New York branch to transfer money and "serve as a 'paymaster' for international terrorists." The transfers helped Hamas and other groups fund attacks and reward families of the perpetrators between 1995 and 2005, the suits alleged.
The bank said in court papers that the U.S. government has called it a constructive partner in the fight against terrorism financing. The bank said only four transactions out of 500,000 involved "designated terrorists" by the U.S. government, and they were the result of machine or human error.
In a separate case, a jury in 2014 found Arab Bank liable for facilitating two dozen militant attacks in Israel. The bank has agreed to settle that case, which arose from a lawsuit brought by Americans under a different federal law, once an appeals court rules on the amount of damages.
The Arab Bank case is the second time the Supreme Court ever has taken up the question of whether companies can be sued under the Alien Tort Statute.
In 2013, the court did not resolve that question when it ruled in favor of Royal Dutch Shell Plc over a lawsuit claiming the company was complicit in a crackdown on protesters in Nigeria.
In that ruling, in the case called Kiobel v. Royal Dutch Shell, the justices instead narrowed the law's reach, saying claims must sufficiently "touch and concern" the United States to overcome the presumption that the Alien Tort Statute does not cover foreign conduct.
The plaintiffs say the relevant corporate activity in the Arab Bank case took place in the United States, thus not foreclosed by the Supreme Court's previous decision.
A ruling is due by the end of June.
(Reporting by Lawrence Hurley; Editing by Will Dunham)