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WASHINGTON, March 14 - Karen P. Hughes, one of President Bush's closest advisers, was nominated today to be under secretary of state for public diplomacy and given the mission of trying to repair the image of the United States around the globe, especially in the Arab world.

"We must do much more to confront hateful propaganda, dispel dangerous myths and get out the truth," Secretary of State Condoleezza Rice said in announcing that the president had turned again to Ms. Hughes, who by all accounts has Mr. Bush's ear and confidence.