Bush said he knew Yushchenko had to keep his word to the people of Ukraine by withdrawing the country's 1,650 troops. Meanwhile, Poland is withdrawing some of its 2,400 troops and Italy will begin pulling out some of its 3,000 member force in September.
Still, Bush but said he accepts Yushchenko's decision.
"The president made clear to me in my first conversation with him that he campaigned [for the Ukrainian presidency] on the idea of bringing some troops out," Bush said. "He's fulfilling a campaign pledge, I fully understand that. But he also has said that he's going to cooperate with the coalition in terms of further withdrawals, and I appreciate that."
Asked how Ukraine would continue to cooperate with the coalition, Yushchenko said that his country's diplomats, business people, and political leaders will carry on what he called the "momentum" begun by Ukrainian peacekeeping troops.
Yushchenko said Ukrainian armed forces already have trained many Iraqi security units and that their own security effort has allowed fully 1,500 people to return to normal life.
Meanwhile, Bush said he will help Ukraine in its effort to join the World Trade Organization by the end of the year and to remove Soviet-era U.S. sanctions on Ukrainian exports. He also said he has asked Congress to approve $60 million in aid to Ukraine.
Further, Bush said the United States backs Ukraine's efforts to join both the European Union and NATO: "The first time I met the president was at NATO during my latest trip to Europe, and my conversation with him there was the same as I had here [with Yushchenko], and that is: There is a way forward in order to become a partner of the United States and other nations in NATO. And it's a path, and we want to help Ukraine get on that path as quickly as possible."
The American leader cautioned, however, that membership in the EU and NATO are not assured. Bush said Ukraine first has much to do on both the economic and security fronts.
Yushchenko and Bush said they found mutual understanding on all the topics they discussed. Both men attributed this to shared values: democracy, a respect for human rights, and the rule of law.
The Ukrainian leader said he believes a democratic Ukraine will be good for Europe, and that U.S. support of Ukrainian democracy will be even better for the continent.