Shoigu made the remarks in a meeting with the Secretary of Iran's Supreme National Security Council (SNSC) Ali Akbar Ahmadian.
"Russia adheres to previous agreements with Tehran regarding Zangzur, and Moscow's policy in this regard has not changed at all," Shoigu said.
Elsewhere in his remarks, the top Russian security official said that Moscow supports the sovereignty and territorial integrity of the Islamic Republic of Iran over the country's trio islands in the Persian Gulf.
Ahmadian is visiting Russia to take part in the 14th Meeting of BRICS High-Ranking Officials Responsible for Security Matters/National Security Advisors.
IRNA