Rasmussen made the comment ahead of a two-day meeting of NATO foreign ministers in Brussels that will, among other things, review plans for the missile-defense system in Europe.
Earlier, the chief of staff of the Russian armed forces said Moscow was being pushed into a new arms race by the planned deployment of the system.
Speaking at a meeting with foreign military attaches, General Nikolai Makarov warned of a possible "sharp deterioration" of relations.
"The very idea of creating a missile-defense system can definitely bring about a sharp deterioration in our relations," Makarov said.
He said that Russia had begun the deployment of new weapons systems in its western exclave of Kaliningrad so that, once a NATO missile shield was operational, the nuclear deterrent between the two sides remained balanced.
Washington says the planned missile shield is meant to prevent a possible attack from countries such as Iran, but Russia fears it will make its nuclear arsenal ineffective.
NATO has rejected Russia's demand to jointly build a missile-defense system.
compiled from agency reports