Morteza Alghosi seized a gold medal in the 130kg weight class, while Vahid Dadkhah won a bronze medal in the 97kg.
Freestylers Mostafa Ghiasi (79kg) and Arashk Mohebbi (92kg) had won two gold medals and Amir Mohammad Yazdani (70kg) seized a bronze.
Greco-Roman wrestler Shahin Bodaghi (72kg) also took a gold medal on the first day.
The 60th edition of the event began on March 2 in Sofia, Bulgaria and will run until March 5.
The tournament is being held in honor of Dan Kolov who was the first European freestyle wrestling champion from Bulgaria and European and world champion Nikola Petrov.