Two former communist countries, Poland and Romania, have opened negotiations on the stationing of American troops on their territories.
Polish and Romanian officials say they are ready to host American military bases, and that further negotiations with Washington are expected shortly.
Both former Soviet satellite states supported the U.S.-led war in Iraq, unlike Germany and France.
Poland, which joined NATO four years ago, has 2,000 troops in Iraq as part of the American and British-dominated coalition.
Polish Defense Minister Jerzy Szmajdzinski says his country is generally in favor of hosting the American bases, although the question of who will cover the operating costs remains to be decided.
Poland's budget has been strained by multi-billion-dollar defense deals last year with the United States, Finland and Israel to bring its Soviet-era army up to NATO standards.
The stationing of American troops will be among the topics discussed by Polish President Aleksander Kwasniewski and President Bush in Washington later this month.
Romania, which is due to become a NATO member later this year, has made clear it, too, would welcome American soldiers. Romanian Prime Minister Adrian Nastase says they would be well-placed strategically because of Romania's access to the Black Sea and proximity to the Middle East.
Romania and its neighbor, Bulgaria, already helped Washington by opening their airspace to U.S. aircraft heading to the war in Iraq.
Hungary, which opened a military base for the training of Iraqi volunteers last year and hosts American forces as part of the nearby Balkan peace mission, said it is also prepared to help the United States.
But Hungary has been criticized by Washington and NATO for not always reacting quickly to emergency military situations. The Hungarian parliament recently made it possible for the government to send peacekeepers abroad without a lengthy parliamentary process.