WASHINGTON — The Supreme Court on Monday ordered a lower court to decide whether Congress has the authority to allow Americans born in Jerusalem to claim Israel as their birthplace on their passports.

The decision postpones resolution of a long-running dispute between Congress and the executive branch over the power to set foreign policy, in this case the highly fraught issue of whether to formally recognize Israel’s claim that Jerusalem is its capital.

At issue is whether Congress overstepped its authority when it passed a law in 2002 requiring that Americans born in Jerusalem be allowed to name Israel as their birthplace in passports and other official documents.

The State Department has refused to enforce the law, saying that it interferes with a matter of foreign policy that is the president’s to decide.

For more than half a century, the United States has not recognized any state as having sovereignty over Jerusalem, a central issue in the intractable diplomatic negotiations between Israel and the Palestinians.

The court, without settling the case on its merits, ruled that the balance of power between Congress and the president in foreign policy was not inherently beyond the reach of judicial review.

With only one dissent, the justices overturned and sent back for reconsideration a decision by the United States Court of Appeals for the District of Columbia Circuit, upholding a district court. The lower courts had thrown out the case on the grounds that the executive branch held exclusive power over the recognition of foreign sovereignty and that its disregard of Congressional instruction could not be challenged in court because the status of Jerusalem was a political question.

The decision, handed down along with a separate ruling in a securities matter, was overshadowed by the long-anticipated opening of three days of oral arguments over challenges to President Obama’s landmark overhaul of the health care system.

The passport case, Zivotofsky v. Clinton, No. 10-699, dealt with a suit brought by the parents of Menachem B. Zivotofsky, who was born in Jerusalem in 2002, not long after Congress passed a law ordering the State Department to record the birthplace of children born in that city as Israel if parents so requested.

When President George W. Bush signed the law, he said he would not follow it, arguing that it “impermissibly interferes” with the president’s power.

The Zivotofskys wanted their newborn son’s American passport to list his country of birth as Israel. Their lawyers argued that doing so would not, in effect, settle the long-disputed and still-unresolved question of Jerusalem’s status. The case presented an unusual instance of the court’s mediating a dispute between the president and Congress over an issue of foreign policy — but the Supreme Court’s action on Monday did not settle the matter, beyond confirming that it was the role of the courts to do so.

Chief Justice John G. Roberts Jr. delivered the majority opinion, joined by Justices Antonin Scalia, Anthony M. Kennedy, Clarence Thomas, Ruth Bader Ginsburg and Elena Kagan. Justice Sonia Sotomayor concurred in part and concurred in the judgment; Justice Samuel A. Alito Jr. concurred in the judgment; and Justice Stephen G. Breyer dissented.

The Obama administration said that the question was one that could be decided only by the president, and that the court should stay out of the matter. Lawyers for the Zivotofskys had contended that what was at issue was the minor matter of an individual’s identity and a passport’s particulars, not an issue of global import. The justices, hearing arguments, seemed skeptical of that claim and focused on whether the judiciary should step in.

Only Justice Breyer reached the conclusion that this was one of the rare cases in which a decision by the executive branch should be beyond review. In many of those cases, he wrote, it is foreign policy matters that earn this designation, either because diplomatic wisdom lies beyond judicial competence, or because in foreign affairs it can be important for the nation to speak with one voice and act in unity.

On a sensitive matter like the status of Jerusalem, Justice Breyer argued, the Zivotofskys had little to gain and the United States government much to lose in the Middle East; he said he would have reached the same conclusion as the appeals court, and bowed out of the dispute.