"Wrestling has brought closer the people of Iran and the U.S.," Jones was quoted saying by the semiofficial Mehr news agency after arriving in Tehran with his team for an international tournament.
American wrestlers will compete in freestyle events later this week after the completion of Greco-Roman matches.
"I am sure the world will become united in support to wrestling and this will lead to change of the view of the OIC. It will keep wrestling in the Olympics," said Jones.
On Monday, U.S. wrestling officials formalized plans for a committee charged with pushing to restore Olympic wrestling — which was dropped earlier this month from the 2020 program by the IOC board. Wrestling now must compete against other sports for one open slot in the Games.
Iran also has said it is looking to join wrestling's major powers to reverse the IOC decision. Last week, the Iranian wrestling federation and Olympic committee sent a protest letter to the OIC.
Iran sees wrestling as their national sport. Since 1948, it has actively participated international events of the sport and its wrestlers have collected many Olympics medals. Iran won three gold medals out of six overall in wrestling at the London Games, and the U.S. took two gold medals out of four overall.
Washington cut ties with Iran after the U.S. Embassy was stormed in the wake of the 1979 Islamic Revolution — with 52 Americans held hostage for 444 days. Tensions are also high over the standoff over Tehran's nuclear program and Western sanctions that have upended Iran's economy.
Iran's state media had only limited reports on the arrival of the American wrestlers — a distinct contrast to the fanfare in 1998 to the first U.S. wrestlers who competed in Iran since the Islamic Revolution.
U.S. sports team make only infrequent appearances in Iran, but the two countries often compete together in international events.
The U.S. has sent more than 30 athletes to Iran under a sports exchange program launched in 2007, and more than 75 Iranian athletes and coaches have visited the United States.