LOS ANGELES, Calif., Jan 31 (Reuters) - Democratic U.S. presidential rivals Barack Obama and Hillary Clinton opened a crucial debate on Thursday by agreeing on one issue: one of them will become president in 2009.

Clinton, who would be the first woman president, and Obama, who would be the first black president, have been locked in a bitter battle for weeks over issues that ranged from health care to race.

The two candidates struck a conciliatory tone on Thursday and said that one of them would take over when President George W. Bush leaves the White House next year.

"It is a testimony to the Democratic Party and it is a testimony to this country that we have the opportunity to make history because I think one of us two will end up being the next president of the United States of America," Obama said, sitting next to the former first lady.

"And I also want to note that I was friends with Hillary Clinton before we started this campaign. I will be friends with Hillary Clinton after this campaign is over," he said.

Clinton, a senator from New York, echoed his comments.

"On January 20, 2009, the next president of the United States will be sworn in on the steps of the capitol," she said. "I, as a Democrat, fervently hope you are looking at that next president. Either Barack or I will raise our hand and swear to uphold the Constitution of the United States."

Before the debate started, Obama stood by the swivel chair meant for Clinton and held it for her, before taking his own seat.

The U.S. general election takes place this November but the winning candidate does not take over until January 2009.

(Reporting by Jeff Mason, editing by Philip Barbara)

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