WASHINGTON — One of the most contentious issues in international diplomacy, the political status of Jerusalem, is proving divisive at the U.S. Supreme Court as well.

Hearing arguments Monday in Washington, the justices clashed along ideological lines over a federal law that would let as many as 50,000 Jerusalem-born U.S. citizens have passports designating their place of birth as Israel.

The Obama administration says the 2002 law infringes the president’s constitutional powers and undermines a longstanding State Department policy of taking no position on Jerusalem’s status. The administration says a decision upholding the law might inflame an already volatile part of the world.

That contention drew support from Justice Elena Kagan, who said Jerusalem is a “tinderbox” right now because of demonstrations over access to a holy site known to Jews as the Temple Mount.

“History suggests that everything is a big deal with respect to the status of Jerusalem,” Kagan said. Palestinians claim the city’s eastern part as a future capital.

Justice Antonin Scalia said the court shouldn’t worry about the foreign-affairs consequences of the case. “The mere fact that it upsets foreign relations doesn’t prove a thing,” he said.

The case may produce the most significant ruling in decades on the balance of power between the president and Congress on foreign affairs.

It comes at an especially tense time for U.S.-Israeli relations. Israeli Prime Minister Benjamin Netanyahu lashed out last week after the Atlantic magazine quoted an unidentified official in President Obama’s administration as calling him a “chickensh-t.” The United States has criticized Israeli plans to speed up construction of 1,000 homes in Jewish parts of east Jerusalem, which Israel captured in 1967.Passports of U.S. citizens born in the city now say only Jerusalem, without mentioning a country.

U.S. Solicitor General Donald Verrilli said the law would force the government to issue thousands of passports that “contradict our official recognition policy and undermine the president’s credibility.” The administration says the Constitution gives the president exclusive power to recognize foreign countries and determine their territorial boundaries.

The Supreme Court case concerns 12-year-old Menachem Binyamin Zivotofsky, whose parents have been trying since his 2002 birth to have his passport indicate he was born in Israel.

The family’s lawyer, Alyza Lewin, said the 2002 law doesn’t challenge the president’s power to make formal recognition decisions. She said the measure merely gives some people the “right to self-identify as they choose that they were born in Israel.”