Raphael Martinetti's resignation was announced at the FILA executive committee meeting in Phuket. The Swiss had been in the position since 2002.
On Tuesday, the executive board of the IOC dumped wrestling from the list of 25 sports guaranteed a berth in future Summer Olympics, meaning it must compete with other fringe sports for a spot on the 2020 program.
FILA member Nenad Lalovic, who has assumed an interim presidency role, confirmed at a news conference that Martinetti's resignation was because of the International Olympic Council's decision.
"It was difficult for a president who was in power for 11 years when the IOC decided to eliminate his sport from the Olympic Games," said Lalovic, adding the new president will soon be elected at an extraordinary congress.
Lalovic said the bid to restore wrestling to the Olympic program would begin immediately.
"Everyone of us will have a duty. We have only one goal that is to be back on the Olympics. Lobbying is very important, but it's not something that you can't determine in advance," Lalovic said. "We have to prepare a serious presentation that must be prepared by professionals to present the real picture of our sport. This sport has been practiced by millions of people. We will use this fact in order to promote our sport."
Now that wrestling is no longer a core Olympic sport, it must compete with seven other contenders — baseball and softball, squash, wakeboarding, sport climbing, roller sports and the martial arts of karate and wushu — in lobbying to earn the last spot on the program for the 2020 Olympics, which have yet to be awarded to a host city.
The IOC executive board will meet in May in St. Petersburg, Russia, to choose which sports to propose for inclusion in 2020. The final vote will be made at the IOC general assembly in September in Buenos Aires, Argentina.
USA Wrestling executive director Rich Bender paid tribute to Martinetti, but said his departure could boost wrestling's chances of getting back on the Olympic program.
"This decision provides international wrestling with an opportunity to change and improve," Bender said in a statement on USA Wrestling's website. "The sport will now be able to create a fresh new relationship with the International Olympic Committee and address some of the pressing challenges and opportunities facing wrestling."
Alexander Mamiashvili, the head of the Russian wrestling federation, wants the FILA extraordinary congress to be held in Moscow in May and said President Vladimir Putin had ordered a committee be formed to contest the IOC decision.
"The group will co-ordinate and analyze the situation to prove wrestling is worthy of staying in the Olympic movement," Mamiashvili told the Itar-TASS news agency of a committee that will include the sports minister and all three Russian IOC members. "The leadership of the country, and personally the president of Russia, has expressed to us their support."
FILA vice-president Stan Dziedzic said he knows what wrestling needs to do to win back its place.
"We need to hire a public-relations firm, we need to have a better relationship with the IOC, obviously. Those are right on top of the table," he said. "We have to tell the world that there is no other sport that is more of a meritocracy than wrestling. No bats, no balls, no gloves; it's not how fast, how far, how high — but how much better.
"Two equal size wrestlers ground on the mat to determine who the best is, with the wits and the will to win. Nothing could be more fundamental."