"We have never allowed them to inspect our nuclear sites or nuclear warheads, and we never will," Ivanov was quoted as saying by Interfax.
Ivanov conceded that Russia was still not up to NATO standards in protecting nuclear material.
"But we believe that we will see NATO ways of nuclear weapons protection from seizure by terrorists next year," he was quoted as telling Russian reporters.
His comments came after some 50 NATO observers came to Russia to oversee military exercises aimed at shoring up the country's line of defense against attacks on the former Soviet-republic's nuclear weapons and energy sites.
During last week's exercises, Ivanov angrily dismissed speculation that Russia's nuclear arsenal was not safe.
"We have never had terrorist attacks on any of our sites," he said in response to a reporter's question last week.
"But unfortunately, myths are spreading in various regions of the world that Russia's nuclear arsenal is of poor quality and unsafe."
The West has expressed increasing concern about the state and safety of Russia's nuclear arsenal amid the troubles of its cash-starved military.
Russian President Vladimir Putin has placed his close ally Ivanov in charge of army reforms and has since promoted him to head the whole massive military infrastructure, demoting the status of the general chiefs of staff.