Both men called for the International Olympic Committee to reconsider after the executive board dropped the sport last month from the program of the 2020 Games.
Wrestling is one of Russia's and Iran's strongest Olympic events.
"The removal from the Olympic program of traditional forms of sports, which were its basis from the beginning and were in the program of the Olympic Games even in the time of ancient Greece ... is unjustified," Putin was quoted by Russian news agencies as saying Wednesday
Putin said he hopes Russia will discuss the issue with the IOC.
Ahmadinejad said he will send a letter to the IOC requesting the decision be reversed.
"Wrestling is compatible with the spirit of the Olympics. The sport combines chivalry, power and speed," he was quoted as saying by Iran's semiofficia Mehr News Agency.
Wrestling's governing body FILA will meet in Moscow on May 18 to elect a new president and make rules changes. Wrestling is now competing with seven other sports for a single opening on the 2020 program, which will be finalized by the IOC in September.