Wrestling has been dropped from the 2020 Games to make way for a new sport.
The International Olympic Committee's executive board made its decision after assessing the performance of all 26 sports at the London Games.
"The news from the IOC is extremely disappointing," said British Wrestling chief executive Colin Nicholson.
There is a slim chance wrestling may win a reprieve when the IOC meets in Buenos Aires in September to ratify its choice.
But it will be vying with seven other sports, among them squash, roller sports and sport climbing, that are hoping for inclusion in the Olympic programme.
Modern pentathlon and taekwondo were thought to be the sports most at risk when the IOC committee met in Lausanne, Switzerland on Tuesday, but wrestling was the surprise choice for the axe.
It will now compete with baseball/softball, squash, karate, sport climbing, wakeboarding, wushu and roller sports for a place in the 2020 Games.
"This is not the end of the process, this is purely a recommendation," said IOC spokesman Mark Adams. "This is not about what's wrong with wrestling but what is good for the Games."
It is extremely unlikely that wrestling will be voted back in so soon after being removed by the executive board, but Adams stressed: "Today's decision is not final."
Wrestling, which combines freestyle and Greco-Roman events, was included in the inaugural modern Olympics in Athens in 1896.
It has been in every Games since then, apart from Paris in 1900. At last year's Olympics, it featured 344 athletes competing in 11 medal events.
Despite Tuesday's news, Nicholson said Great Britain would not lose focus in the next Olympics in Rio de Janeiro.
"We will be looking to deliver success in 2016," he said. "We have two athletes who we believe are genuine medal contenders."
Nicholson also pointed out that wrestling remains part of the Commonwealth Games.
"We are fortunate that we are a Commonwealth sport so our athletes will continue aspiring towards 2014 and 2018," he said.
"In the meantime, we will remain hopeful that the IOC may give wrestling another chance to remain part of the Games."
Before making its decision, the IOC's programme commission assessed each sport by looking at such factors as TV ratings, ticket sales, anti-doping and global popularity.
Klaus Schormann, president of modern pentathlon's governing body, said he had lobbied hard to protect his sport's Olympic status.
"We have promised things and we have delivered," he said. "That gives me a great feeling. It also gives me new energy to develop our sport further and never give up."
GB Modern Pentathlon chief executive, Jon Archer, expressed relief at the news that his sport had been spared.
"Olympic inclusion is absolutely essential to our sport," he said. "It is at the centre of everything we do. We can relax now and work to continually modernise the sport and raise awareness."
Samatha Murray, who won silver for GB in the Modern Pentathlon at London 2012, said on Twitter: "This is a very sad day for wrestling. However I want to thank the IOC's decision to keep #ModPen in the OG for 2020. I'm elated. Thank you."
Golf and rugby sevens will be part of the programme for the 2016 Games in Rio de Janeiro after winning inclusion in 2010.
The IOC will also decide in September whether Istanbul, Madrid or Tokyo will host the 2020 Games.