Ivanov also criticized the what he said were North Atlantic Treaty Organization's mistakes in Afghanistan and Kosovo, as well as US policies in Iraq.
"Rest assured, our attitude is calm but negative," said Ivanov, speaking in English to academics and reporters at a Washington think-tank.
"There is still a window of opportunity between NATO and Russia, and it is up to NATO and first the US to prevent this window from getting completely shut," he said.
Ivanov, who met earlier with US Secretary of Defense Donald Rumsfeld, reminded the audience of Russian cooperation following the September 11 attacks in the United States.
"This cooperation in counterterrorism is more important than our tactical disagreements," he said, alluding to disagreements over the US-led invasion of Iraq.
But now "the occupied Iraqi territory has become the center of attraction for terrorist organizations of the whole world, acting like a magnet for extremists of all sorts," he said.
In Afghanistan, Ivanov noted progress in the fight against illegal drugs, but believes that the drug trade infrastructure still needs to be smashed.
It would be "naive to believe a significant part of that money does not flow to terrorist organizations," he said.
"NATO activities need to be more open to Russia, protecting Europe from a massive flow of heroin," he said.
Concerning Kosovo, he noted that attempts to restore stability "have ended in failure," and that NATO is in part to blame.
At the end of his presentation Ivanov said that Russia's position "is not one of a malevolent observer gloating on NATO difficulties."
Despite disagreements with the Alliance, "we offer our partnership towards global security," he said.
Ivanov's visit follows NATO's biggest expansion ever, during which it welcomed Bulgaria, Estonia, Latvia, Lithuania, Romania, Slovakia and Slovenia.
Moscow has made no effort to hide its irritation at NATO's enlargement, especially at the inclusion of the Baltic states, which used to be part of the Soviet Union.