President Bush says the United States wants a strong Atlantic alliance and is committed to a united Europe.
Speaking in the Polish city of Krakow, in an outdoor courtyard of Wawel palace, Mr. Bush said the forces of aggression and terror must not be appeased, but opposed.
He said the greatest threat to world peace is the spread of nuclear, biological and chemical weapons. Mr. Bush warned against stirring up what he called "new divisions" in NATO and called on its members to stand with the United States in facing the new enemy.
Earlier, the president visited the former Nazi death camps of Auschwitz and Birkenau and called them a sobering reminder of the power of evil and the need for people to resist it.
Mr. Bush held talks with President Aleksander Kwasniewski and thanked Poland for its support in the war against Iraq.
Later Saturday Mr. Bush flies to St. Petersburg, Russia, to take part in the city's 300th anniversary celebrations. There, he will meet with Russia's President Vladimir Putin, French President Jacques Chirac and German Chancellor Gerhard Schroeder for the first time since the Iraq war, which they opposed.
Mr. Bush told European journalists this week that he wants to heal trans-Atlantic rifts over the Iraq war.
On Sunday Mr. Bush attends the G-8 summit in Evian, France, then travels to the Middle East to promote the internationally-backed "road map" to peace in the region.
Mr. Bush will first go to Egypt for talks with Arab leaders and then to Jordan for a three-way summit with Israeli Prime Minister Ariel Sharon and his Palestinian counterpart, Mahmoud Abbas.