WASHINGTON, May 2 (James Vicini/Reuters) - The US Supreme Court said on Monday it would hear an appeal by parents who want Secretary of State Hillary Clinton to record Israel, not just Jerusalem, on their son's US passport.

The justices will consider whether lower court judges were correct to dismiss the lawsuit on the grounds that it raised a foreign policy issue falling outside the judiciary's power.

The case involves Menachem Zivotofsky, a US citizen born in 2002 in Jerusalem. His mother asked that his passport and other documents list his place of birth as Jerusalem, Israel.

US diplomatic officials told her that State Department policy required them to record only Jerusalem as his place of birth because the United States does not currently recognize any country as having sovereignty over Jerusalem.

While Israel calls Jerusalem its eternal and indivisible capital, few other states accept that status. Most countries including the United States maintain their embassies to Israel in the coastal metropolis of Tel Aviv.

The Palestinians want East Jerusalem, captured by Israel in 1967, as capital of the state they aim to establish in the West Bank and Gaza Strip, alongside Israel.

Jerusalem is home to the holiest sites in Judaism and Christianity and the third holiest site in Islam.

Zivotofsky's mother and father, Naomi and Ari, filed a lawsuit in 2003 in federal court in Washington over the passport rule. A federal judge dismissed the case because it involved an issue beyond the judiciary's power.

An appeals court agreed, saying judges have no authority to order the federal government to change US foreign policy.

The Obama administration opposed the appeal.

The status of Jerusalem is one of the most sensitive and long-standing disputes in the Arab-Israeli conflict, Acting Solicitor General Neal Katyal told the Supreme Court.

He said the US president and the government's executive branch have sole power in foreign affairs to decide policies about passports for US citizens born in Jerusalem.

The Supreme Court is expected to hear arguments and then rule in the case in its upcoming term that begins in October.

The case is Zivotofsky v. Clinton, No. 10-699.

(Reporting by James Vicini, Editing by Laura MacInnis)