WASHINGTON  The Supreme Court on Monday revived a lawsuit brought by four former prisoners at Guantánamo Bay against Donald H. Rumsfeld, the former defense secretary, and other officials. The former prisoners, all British citizens, say they were tortured and subjected to religious persecution.

In a brief order, the justices instructed a federal appeals court to take a second look at the case in light of the Supreme Court’s decision in June in Boumediene v. Bush granting Guantánamo prisoners the right to challenge their detention in federal court.

The appeals court, the United States Court of Appeals for the District of Columbia Circuit, ruled against the men in January, saying that neither the Constitution nor a federal law protecting religious freedom gave them the right to sue in American courts.

In urging the Supreme Court not to hear the case, the Justice Department said the Boumediene decision “did not overturn the court’s prior rulings that the individual-rights provisions of the Constitution run only to aliens who have a substantial connection to our country and not to enemy combatants who are detained abroad.”