NATO Secretary General Anders Fogh Rasmussen said on Wednesday that the alliance and Russia should cooperate on missile defense to boost mutual trust and security.

He made the remarks in an online video, one week after U.S. President Barack Obama and Russian President Dmitry Medvedev signed a landmark nuclear arms treaty in the Czech capital of Prague, committing to significant reductions in their countries' atomic arsenals.

"The United States and Russia now are clearly seeing eye-to-eye on a range of security issues and we should use this new momentum to take further steps to enhance our common security. Together, NATO and Russia should explore cooperation on missile defense, a security roof that will give real security to our people," Fogh Rasmussen said.

"I believe this is the most significant step we can take to integrate Russia more fully in Euro-Atlantic security. It would demonstrate on a daily basis that we cooperate and exchange information to counter rising threat of missile proliferation. We would develop trust and prevent hostility between NATO and Russia, " he said.

He said that "missile defense is the right answer to some of the most important challenges we are facing and a strong contribution to our shared security, including disarmament."