Interfax news agency quoted Deputy Russian Foreign Minister Andrei Rudenko as saying Iran's proposal was made by Iran’s Deputy Foreign Minister Abbas Araqchi during a visit to Moscow last week, but gave no details.
"We're looking carefully at it," Rudenko told journalists, Reuters reported.
The Iranian official began a regional tour last Tuesday with the aim of promoting the Tehran’s initiative. He visited Azerbaijan, Russia, Armenia and Turkey.
At least 1,000 people, and possibly many more, have been killed since fighting broke out on Sept. 27 in Nagorno-Karabakh, an enclave internationally recognized as part of Azerbaijan but populated and controlled by ethnic Armenians.
The war is the worst fighting in more than 25 years in the region that was once part of the Soviet Union and long dominated by Moscow.
Negotiations have for decades been led by Russia, France and the United States in their roles as co-chairs of a panel known as the Minsk Group of the Organization for Security and Cooperation in Europe (OSCE), a security and rights watchdog.
Within hours of an agreement being reached with the warring sides on Friday not to target civilians, attacks resumed, and concerns remain about the security of oil and gas pipelines in Azerbaijan.
Last week, Tehran introduced an initiative for resolution of the conflict in Nagorno-Karabakh region. Iran is neighboring Azerbaijan and Armenia.