There is an international wrestling meet scheduled for May in Times Square, an annual contest pitting top Americans against international stars. But it is not clear if Iranians will be granted sports visas to compete.

Mr. Trump’s order bars visitors from seven nations: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.

Nenad Lalovic, the president of United World Wrestling, the international federation, said in a statement: “Though we had hoped for a different outcome from Iran’s Foreign Ministry, we appreciate the complex nature of this decision. We are currently working to find a solution for the Freestyle World Cup as soon as possible.”

“United World Wrestling hosts a full calendar of events every season, and we’re certain to see American and Iranian wrestlers on the same mat again in the very near future,” it added.

Mr. Trump’s order is a complicated issue for the United States Olympic Committee, which calls itself “the steward of the Olympic movement in the United States.” The organization does not want to antagonize the president, so its response has been relatively muted. The committee is invested in a bid to bring the 2024 Summer Games to Los Angeles, and that bid’s chances have been damaged by the executive order, which alarmed some of the International Olympic Committee members who will select the host city.

“We are disappointed for our wrestlers, who have been warmly welcomed by the Iranian public on many occasions,” said Patrick Sandusky, a spokesman for the United States Olympic Committee.