It said it has always complied with IOC regulations and is represented in 180 countries, with wrestling the national sport in some of them.
The federation, which is headed by Raphael Martinetti and based in Corsier-sur-Vevey, Switzerland, said it would meet next week in Thailand to discuss the matter.
Gardner cited wrestling's worldwide popularity and urged a campaign to keep it in the Olympics.
"It just seems like wrestling — if we don't fight, we're going to die," he said. "At this point, it's time for everybody to man up and support the program."
The decision hit hard in Russia, which has long been a power in the sport.
Mikhail Mamiashvili, president of the Russian Wrestling Federation, suggested FILA had not done enough to keep the sport in the games.
"We want to hear what was done to prevent this issue from even being discussed at the board," he said on the Rossiya TV channel.
In comments carried by ITAR-Tass, Mamiashvili added: "I can say for sure that the roots of this problem is at the FILA. I believe that Martinetti's task was to work hard, socialize and defend wrestling's place before the IOC."
Alexander Leipold, a 2000 Olympic champion from Germany and former freestyle German team coach, said he was shocked.
"We are a technical, tactical martial sport where the aim is not to harm the opponent," he said. "Competing at the Olympics is the greatest for an athlete."
Wrestling's long history in the Olympics has featured some top names and moments:
— Karelin won the super-heavyweight gold in Greco-Roman over three straight Olympics — 1988, 1992 and 1996 — until his streak was ended by Gardner, who beat him for the gold in 2000.
— Baumgartner won four Olympic medals, including golds in 1984 and 1992.
— Blatnick overcame cancer to win gold in Greco-Roman at the 1984 Los Angeles Games, bursting into tears after the match. Blatnick died last year at age 55.
— Burroughs emerged as the star of the sport in London, where he won the 74-kilogram gold.
The last sports removed from the Olympics were baseball and softball, voted out by the IOC in 2005 and off the program since the 2008 Beijing Games. Golf and rugby will be joining the program at the 2016 Games in Rio.
Among those in Lausanne were the leaders of the recently created World Baseball Softball Confederation. The two sports agreed last year to merge in a joint bid to return to the games.
Don Porter, the American who heads international softball, and Riccardo Fraccari, the Italian who leads baseball, are working out the final details of their unified body ahead of their presentation to the IOC in May.
A major hurdle remains the lack of a commitment from Major League Baseball to release top players for the Olympics.
Porter and Fraccari said they hope to have another meeting with MLB officials in April in Tokyo.
"The next thing is to sit down with them and see how they can help us," Porter said. "It all depends on the timing, the timing of the season. It's not an easy decision to allow players a week off."
Associated Press writers Lynn Berry in Moscow and Luke Meredith in Des Moines, Iowa, contributed to this story.
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