"We knew even before whichever sport will not be included would lead to criticism from followers of that sport," IOC President Jacques Rogge said. "I had contact with the FILA (international wrestling federation) president and we agreed to meet at the first opportunity.
"They have reacted well to this disheartening news. They vowed to adapt the sport, to fight to be included in 2020.
"The vote of yesterday is not an elimination of wrestling from the Olympics, I want to be clear on that. Wrestling will be at the (Rio de Janeiro) 2016 Games and to the athletes I say continue to train for Rio and your federation is working towards inclusion in the 2020 Games."
The IOC's 15-member executive board voted on Tuesday to recommend that the sport be dropped from the 2020 Olympic programme, with a final decision resting with the IOC session in September in Buenos Aires.
The IOC is eager to revamp its sports programme to keep it relevant to a new generation of viewers, fans and sponsors.
The vote prompted an instant wave of protest and anger from the sport's global community with FILA calling it an aberration, petitions launched with the United States White House and on-line wrestling support groups signing up thousands of supporters.
The Greek Olympic Committee urged the IOC to reverse its decision regarding the sport that was practised at the ancient Games and was part of the first edition of the modern Olympics in 1896.
"This is undoubtedly a decision against the history of the Olympics and of sports in general," the HOC said in a statement.
The IOC holds its Olympic torch-lighting ceremony for the modern Games in ancient Olympia, metres from the gymnasium used by wrestlers in ancient Greece.
"There needs to be a reconsideration of this decision after careful study," the HOC said.
India's government said on Wednesday the decision was "unfortunate and shocking" and it would seek the support of other countries where wrestling is popular to help the sport remain an Olympic discipline.
"These reactions, they are quite normal," IOC Vice President Thomas Bach said. "This would have happened with any decision. You have to find the right balance between tradition and progress.
"This was a decision about core sports and nothing more," he said of Tuesday's vote that cut the core Olympic sports from 26 to 25, leaving out wrestling.
"Keep in mind a final decision has not yet been taken. If they (FILA) continue like that they will win a lot of sympathies," said Bach, a potential presidential candidate later this year.
The IOC's executive board will meet in St Petersburg in May to decide which of eight candidate sports, including wrestling, will be put forward to win the spot left vacant for the 2020 Games.
It will then put its recommendation for the 25 core sports and the new entry to a vote at its session in Argentina.
"It was always going to be a painful decision," IOC member and head of the organisation's finance commission Richard Carrion, also a potential presidential candidate, said.
"No matter what we do, it will be criticised by someone," said Puerto Rican Carrion, whose country won a silver medal in wrestling at the London 2012 Olympics, one of two medals overall.
"From a personal point of view I am sad. I have become attached to the wrestling club (in Puerto Rico) which doesn't even have a regulation-size mat and still managed to send three athletes to the Games."
For Juan Antonio Samaranch Junior, who is both an executive board member and a modern pentathlon vice-president, the decision was a good one.
"I am very sorry for wrestling as it is a sport I respect," the son of former IOC president Samaranch, said.
"I cannot be surprised by the reaction because any sport would have created the same reaction."
Wrestling's surprise exit has been blamed by some on a lack of political support within the executive board, where other sports at risk - including modern pentathlon and taekwondo - had the upper hand with representatives in the 15-member group.
Asked whether his double capacity was a conflict of interest, Samaranch said: "I am here in my capacity as executive board member."