Rasmussen was speaking after a meeting of NATO's 28 foreign ministers with Russian Foreign Minister Sergei Lavrov in Brussels.
He said that "differences remain" but that both sides agreed that it is important "to keep on talking."
"On missile defense, we do not agree yet. But we all agree that it is important to keep on trying. To keep on talking. And to keep on listening to each other's concerns," Rasmussen said. "Because that is the spirit of Lisbon. And because we know that, if we can reach agreement on this issue, it will take our relationship to the next level."
Russia was said to be seeking guarantees that any possible missile shield wouldn't be used against Russia and wanted to be involved in the planning.
Lavrov, in comments ahead of the meeting, complained that Russia's "legitimate demands are not taken into account."
Also speaking ahead of the meeting, Rasmussen had said "one area where there continues to be a need for dialogue is missile defense."
He noted that more than 30 states have or are developing missile technology and "some of these missiles can already reach parts of Alliance territory...and that is why NATO has taken a decision to build its own system."
NATO says the planned missile shield is intended to ward off attacks from countries such as Iran.
compiled from agency reports