(Refile to fix name of Letterman show)

NEW YORK, Sept 21 (Reuters) - U.S. President Barack Obama said on Monday he will decide whether to deploy more troops to Afghanistan when he is certain of U.S. strategy.

"We're not going to make any decisions on further troop deployments until we know what exactly is our strategy," he said in an interview on the "Late Show with David Letterman" television program. Obama said he would be asking tough questions of his national security team.

(Reporting by Matt Spetalnick, editing by Bill Trott)

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