WASHINGTON—Challengers to President Donald Trump’s travel ban targeting several Muslim-majority countries on Thursday urged the U.S. Supreme Court to decide the policy’s legality even though it has been replaced with a revised plan.

In separate letters to the court, the American Civil Liberties Union and the state of Hawaii said the justices should still hear the case, which had been scheduled for arguments next week but was taken off their calendar after the administration announced the reworked ban last month.

The challengers, characterizing the new ban as an indefinite extension of the previous one, said individuals who sued have an interest in the expired measure being declared unlawful because they continue to be harmed by the new policy.

Hawaii also told the court in a separate letter that it intended to challenge Trump’s latest travel ban by seeking on Friday to amend its existing lawsuit against the previous one.

The Justice Department urged the justices not to hear the case, to throw out earlier lower court rulings that had invalidated the ban and to order that the legal challenges be dismissed.

Trump’s three successive moves to block entry into the United States by people from several predominantly Muslim countries have been among his most contentious acts since taking office in January. Trump had promised as a candidate “a total and complete shutdown of Muslims entering the United States.”

The ACLU told the court that the plaintiffs who sued to stop the policy “retain an all-too-real stake in the outcome of the case” even though the original 90-day travel ban on people from six countries expired on Sept. 24. That order was signed by Trump in March and was enacted with some changes in June with the high court’s blessing.

A separate 120-day ban on refugees entering the United States that was part of Trump’s March order expires on Oct. 24.

The weekly behind-closed-doors meeting in which the justices consider next steps in cases before them is scheduled for Friday morning. The court could make an announcement at any time.