CAS, which did not say when a hearing could take place, confirmed the federation was looking to void the IAAF's decision in July to prolong the ban and regain Russia's full IAAF membership as soon as possible.
Russia's athletics federation was suspended in November, 2015 after a report commissioned by the World Anti-Doping Agency (WADA) found evidence of systematic, state-sponsored doping in the sport.
Although Russia has pledged to co-operate with global sports bodies to curb the use of banned performance-enhancing drugs, the authorities have vehemently denied the existence of state-sponsored doping cover-ups.
The federation's legal action came days after WADA conditionally reinstated Russian anti-doping agency RUSADA, angering sports bodies around the world.
The move fulfilled one of three pre-conditions that need to be met for the IAAF to reinstate the suspended federation.
For the federation to be reinstated, Russia must acknowledge that officials from the Sports Ministry were involved in doping cover-up schemes. Russian authorities must provide access to data from testing samples at the Moscow lab, which was also suspended following the 2015 scandal.
The IAAF said on Wednesday it was confident in its legal position and that the Russian federation could only be reinstated if the outstanding criteria were met.
The IAAF will discuss Russia's progress towards reinstatement at its next council meeting in Monaco in December.
Despite the federation's suspension, some Russian athletes -- including 2015 world champion 110 metres hurdler Sergey Shubenkov and twice world champion high jumper Maria Lasitskene -- have been cleared to compete internationally as neutrals after demonstrating they train in a doping-free environment.
(Reporting by Gabrielle Tétrault-Farber,; Editing by Ed Osmond)
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