Styles (FILA) has vowed to fight the decision, while multiple medallists Russia and Iran have also said they hoped the IOC would backtrack.
"This issue will definitely be a big blow to the country's sport, as it is one of our country's most popular sports," the head of Iran's national Olympic commitee, Mohammad Aliabadi was quoted as saying in Iranian media.
"I will certainly pursue the case."
IOC president Jacques Rogge meanwhile insisted today that the vote -- by secret ballot -- was fair and said he understood the angry response from those involved in the sport.
A meeting was planned between the committee and the International Federation of Associated Wrestling Styles (FILA), to discuss the matter, he told a news conference in Lausanne.
Wrestlers have been left dismayed by the decision, with Japan's undisputed queen of the ring, Saori Yoshida, saying: "I am so devastated that I don't know what to do."
Yoshida, a 55kg-class freestyle wrestler who is the face of Tokyo's campaign for the right to host the 2020 Games, has won a record 13 straight Olympic and world championship gold medals over 10 years.
In India, Sushil Kumar, who won a bronze in Beijing and a silver in London last year, said: "I still can't get over the news that we won't be at the Olympics.
"All sportsmen look towards the Olympics as the pinnacle of excellence, everyone wants to take part in them. Now what do we do? Give up wrestling? I hope the IOC will reconsider this decision."
An online petition at change.Org entitled "The International Olympic Committee: Save Wrestling as an Olympic sport #SaveOlympicWrestling" has also been mounted, urging the US Senate to take up the matter.
By late afternoon today, it had more than 21,000 signatures. On Twitter, one user, @WrestlersLoveUs, wrote: "Ancient Olympic wrestlers used to sometimes fight to the death. IOC better understand we're ready to do that again. #SaveOlympicWrestling." AFP AH
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