UPDATE 1-Israel, Palestine discuss peace in private -Rice

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WASHINGTON, May 18 (Reuters) - Israeli and Palestinian negotiators are privately discussing a peace agreement and the talks should intensify in the next several months, U.S. Secretary of State Condoleezza Rice said on Sunday.

"I do know how seriously they are discussing all of the key issues," Rice told reporters aboard Air Force One as she returned from a Middle East trip with President George W. Bush. "I think you're going to see them intensifying those discussions over the next several months."

There have been few obvious signs of progress toward a peace deal six months into negotiations sponsored by U.S. President George W. Bush and Arabs were dismayed by his outspoken support for Israel during a visit there last week.

After Bush's visit, Israelis used some of their toughest language yet to insist that Palestinians would have to abandon 60-year-old refugee claims if they want to establish their own state.

Rice said negotiations were continuing behind closed doors.

"I can tell you for certain that there is more going on in private but that's the way people actually negotiate," Rice said.

"They're not going to talk in front of the cameras about what it is they're doing and if they did, the negotiations would be dead on that day," she said. (Reporting by Tabassum Zakaria; Writing by Andy Sullivan; Editing by Bill Trott)