Bush made the remarks during a visit to a U.S. military base in Kuwait that came on the third day of a weeklong tour of the Persian Gulf, where he is seeking support for an Israeli-Palestinian peace settlement and also for containing Iran.
Bush was briefed by General David Petraeus, the top U.S. military commander in Iraq, and the U.S. ambassador to Iraq, Ryan Crocker, at Camp Arifjan in Kuwait.
After the talks, Bush told journalists that hope is returning to Iraq following the increase in U.S. troop levels by 30,000 last year. The U.S. president said further reductions of troop levels beyond the planned 20,000 will depend on conditions on the ground and stressed that is up to Petraeus to decide whether such a move is possible.
"There is no doubt in my mind that we will succeed," Bush told some of the 15,000 troops stationed at Camp Arifjan, which serves as a staging ground for forces deploying to Iraq. "There's no doubt in my mind, when history is written, the final page will say, 'Victory was achieved by the United States of America for the good of the world.' And by doing the hard work now, we can look back and say the United States of America is more secure and generations of Americans will be able to live in peace."
Asked in a January 11 interview with NBC television whether the U.S. military presence in Iraq might last 10 years, Bush said, "It could easily be that, absolutely."
Bush was scheduled to continue his regional tour to Bahrain, Saudi Arabia, and the United Arab Emirates.
Bush's broader Mideast visit follows his first visit as president to Israel and the West Bank, where he sought to encourage progress toward an Israeli-Palestinian peace agreement before his term in office ends in January 2009.
Bush's Middle East tour ends in Egypt on January 16.