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President Bush, speaking at a news conference after Democrats won control of the House of Representatives from his Republican Party, said he and Rumsfeld agreed that a "fresh perspective" was needed on Iraq. The election outcome was widely seen as voters' rebuke to the handling of the unpopular war.
>>Rumsfeld quits after Republicans routed
But Bush said his party's election defeat did not mean the United States would withdraw prematurely.
"The enemy is going to say 'well, it must mean America is going to leave. And the answer is 'no,'" Bush said.
Bush insisted he remained "committed to victory" in Iraq but acknowledged things were not going as well as he wanted.
Commenting on his discussions with Rumsfeld leading up to the resignation decision, Bush said, "He himself understands Iraq is not working well enough, fast enough."
But Bush insisted that US troops would not leave before their mission was complete.
"It's a tough fight," he said. "We're going to win the fight."
- REUTERS