"The fundamental question is: is it worth it? And the answer is, Absolutely it's worth it for a free Iraq to emerge," Mr. Bush said, standing alongside visiting Ukrainian President Viktor Yushchenko.
Yushchenko is withdrawing Ukraine's troops from Iraq.
Mr. Bush said that it doesn't bother him that Yushchenko is pulling his troops out, following a campaign promise that Yushchenko made last year.
Mr. Bush said the U.S.-led coalition's strategy in Iraq remains to train Iraqi soldiers and security forces so they can defend their own country.
"The president made clear to me in my first conversation with him that he campaigned on the idea of bringing some troops out. He's fulfilling a campaign pledge. I fully understand that," Mr. Bush said.
"But he also said he's going to cooperate with the coalition in terms of further withdraws," he added. "And I appreciate that."
Yushchenko has begun withdrawing Ukraine's 1,650 troops.
Mr. Bush said he appreciated the job that Ukrainian forces did in helping protect Iraqis vote in January.
Mr. Bush promised to support Ukraine's bid to join the World Trade Organization by the end of this year and to seek to persuade Congress to lift remaining trade restrictions on Ukraine that are a vestige of the Cold War.
"In America, you've got a strong friend," Mr. Bush said.