“We now have come face to face with our biggest challenge, one that will determine the future of our sport,” said Nenad Lalovic, the acting president of FILA, the sport’s governing body. “We love our sport, and we are united to save it.”

The executive board of the International Olympic Committee recommended in February that wrestling be dropped as one of the 26 core sports in the 2020 Olympic Games (a host city has yet to be named). A final vote is scheduled in September, and the appearance of the three teams together at the United Nations and at Grand Central is part of the marketing effort to preserve it.

To save the sport, the Olympic committee has stipulated that the world’s wrestling associations enact some changes, like making the rules easier to understand and including more women in management. In general, the idea is to make wrestling more accessible and exciting to attract a larger audience. (Men — and some women — in tight singlets are apparently not enough.)

Hence the choice of Grand Central. “This is a great example of pushing the envelope on how to present our sport differently,” said Rich Bender, the executive director of U.S.A. Wrestling, the national governing body for amateur wrestling.

It is not the first such competition. The United States has sent teams to Iran almost a dozen times, and Iran has reciprocated. In February, Jordan Burroughs, 24, the American Olympic gold medalist, said he was mobbed in Tehran by screaming fans when he went for the World Cup. Even President Mahmoud Ahmadinejad showed up to shake his hand.