The president of the All-Russia Athletics Federation (ARAF) Dmitry Shlyakhtin claims Russian athletes will be unable to compete at the Rio Olympics if an IAAF ban is not lifted by June.
Russia was suspended from international competition by athletics' governing body in November following allegations of state-sponsored doping in a report from an independent commission established by the World Anti-Doping Agency.
The IAAF subsequently produced a list of criteria that ARAF must comply with in order to have its ban overturned.
Shlyakhtin remains confident that Russian athletes will be allowed to compete in Brazil.
"We believe that our team will perform at the Olympic Games. We hope so," he is quoted as saying by R Sport.
"But we understand that there is a point of no return. That is June."
Shlyakhtin, elected as president last month, says Russian athletes are continuing to train in preparation for Rio.
"The Olympic Games without the Russian national team, this is not the Olympic Games," he added.
"Our athletes continue to train. We believe and hope that justice will prevail."