Mohmadi lost to Bulgarian Semen Novikov 7-0 in the 87kg final.
Iranian wrestlers Mohammadhadi Saravi (97kg) and Saeid Esmaeili (67kg) have previously won two gold medals.
Amin Mirzazadh has also claimed a bronze medal in 130kg.
Greco-Roman wrestling has been a blue-ribbon Olympic event ever since the first modern Games were held in Athens in 1896. It became a permanent fixture on the Olympic program in 1908.
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