The U.S. announced plans in January to deploy interceptor missiles in Poland and a missile defense radar in the Czech Republic as part of its missile shield aimed at countering possible threats from "rogue states" such as Iran and North Korea.
Witold Waszczykowski, a Polish deputy foreign minister said that the talks are "a discussion between allies, and not belligerent parties, which want to get something at the expense of the other."
He also said that many questions remain to be answered, but that "the current meeting fills us with optimism."
Russia, infuriated by the idea of a U.S. missile shield in the territories of its former ally states, has repeatedly condemned the plan, claiming that it could be a "destabilizing factor" and threaten Russia's national security, and warning that "appropriate measures" would be taken in response.
Russia's foreign minister said Tuesday the plans jeopardize not only Russia, but the whole of Europe.
However, U.S. President George W. Bush insists that the plans are not directed against Russia.