Mohammad Baqer Qalibaf and Vyacheslav Viktorovich Volodin held a telephone conversation on Monday.
The two senior lawmakers discussed the most recent developments in Tehran-Moscow relations and regional issues.
On Friday, Iranian Foreign Minister Mohammad Javad Zarif and his Russian counterpart discussed the recent developments in Nagorno-Karabakh amid a flare-up of fighting between Armenia and the Republic of Azerbaijan over the disputed region.
Tehran and Moscow have called on the warring sides to cease hostilities and hold talks.