Russian President Vladimir Putin said he proposed during a meeting with US President George W Bush expanding cooperation on a missile shield to include Europe and NATO.
The Russian leader also disagreed with Bush saying that he did not believe it was necessary to have the missile defense systems in Poland and the Czech Republic.
Mr Bush is hosting his Russian counterpart for informal talks at the Bush family holiday home in Kennebunkport in the US state of Maine.
Relations have been strained recently between the two countries and the talks are aimed at easing tensions.
The UN-administered province of Kosovo is another issue on which the two sides disagree.
President Bush is also expected to raise the issue of Iran, hoping to gain Russian support for wider economic sanctions aimed at pressuring Iran over its nuclear programme.
