WASHINGTON, Sept 13 (Reuters) - President George W. Bush on Thursday will tell the American public his strategy in Iraq is working and will allow the military to begin reducing U.S. troop levels there.

But he will also say the size of the troop cuts will hinge on continued progress.

"The more successful we are, the more American troops can return home," Bush will say in a televised address to the nation, according to excerpts released by the White House.

Bush also plans to say the Iraqi government has not met its legislative benchmarks and "I have made it clear that they must."

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