SAN ANTONIO, Texas, March 3 (Reuters) - Democratic U.S. presidential candidate Barack Obama on Monday backed the Bush administration's policy of shunning contact with the Islamic militants of Hamas in its Middle East peace diplomacy.

The Illinois senator has said he would break with President George W. Bush's stance of declining to talk to some other international adversaries but that stance does not apply to Hamas, which controls the Gaza Strip and is committed to the destruction of Israel.

Obama has said in the past he would be willing to meet with leaders with whom the Bush administration strongly disagrees, including Iranian President Mahmoud Ahmadinejad and Cuban leader Raul Castro.

Obama, hoping to win his party's nomination to face likely Republican nominee Sen. John McCain in the November presidential election, said his willingness to meet with foes "does not include Hamas."

"You can't negotiate with somebody who does not recognize the right of a country to exist so I understand why Israel doesn't meet with Hamas," Obama told reporters during a campaign stop in San Antonio, Texas.

Iran does not recognize Israel either and its president has often threatened the imminent destruction of the Jewish state, drawing criticism from the West which fears Iran wants to make nuclear bombs that could threaten the region.

U.S. Secretary of State Condoleezza Rice left for the Middle East on Monday to try to salvage U.S.-sponsored peace talks derailed by Hamas rocket attacks on Israeli towns and Israel's military response in Gaza.

"I do think it is important to us to try to jump-start the peace process," Obama said. "It has been under enormous strain of late." (Writing by Caren Bohan; Editing by Alan Elsner)

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