In their meeting, the two ministers conferred on regional issues, the ongoing crisis in Syria in particular.
Muallem arrived in Tehran on Tuesday to be part of the high-level negotiations underway in Tehran on the developments in the Middle East.
Russian Deputy Foreign Minister Mikhail Bogdanov also arrived in Tehran on Tuesday to hold talks with Iranian officials and take part in the negotiations.
The Syrian and Russian officials held a bilateral meeting on Tuesday on ways to resolve the crisis in the war-torn Arab country through regional cooperation.
Muallem had earlier on Tuesday held a meeting with Iranian Deputy Foreign Minister for Arab and African Affairs Hossein Amir Abdollahian, during which the two sides discussed counter-terror efforts and the latest regional developments.
“Any initiative (to resolve the Syrian crisis) should be implemented in coordination with Syrian authorities,” the Syrian minister had said in the meeting.
Syria has been gripped by civil war since March 2011. In the past four years, more than 200,000 people have died in Syria -overwhelmingly civilians– and around 4 million Syrian people are now refugees in other countries. Another 7.6 million are displaced inside Syria.