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The International Paralympic Committee (IPC) confirmed last week that the entire Russian team would be banned following the McLaren report.
That report, published last month, detailed a state-sponsored doping programme operated by Russia.
Rio's Paralympics begin on 7 September, with 267 Russian competitors across 18 sports set to miss the Games.
The appeal hearing is set for 21 August with a decision expected on 22 August.
The IPC's decision was in contrast to the International Olympic Committee (IOC), which chose not to hand Russia a blanket ban from the Olympic Games.
Announcing the decision, IPC president Sir Philip Craven said Russia's anti-doping system was "broken, corrupted and entirely compromised".
In response, Russian Paralympic Committee president Vladimir Lukin said his group was "not even mentioned" in the McLaren report and this action would mean "lives are broken".
"Inevitably, suspicions arise that this is provoked by something unsportsmanlike, something else," he added.
"We absolutely do not want to quarrel, get carried away with emotions. Only the weak get carried away with emotions.
"We will stand our ground in a civilised way."
Richard McLaren, a Canadian law professor, published a report that found Russia's sports ministry manipulated urine samples provided by its athletes between 2011 and 2015.
The report identified 27 samples relating to eight Para-sports, five of which are summer sports, including some governed by the IPC.
The IPC also found evidence that samples were swapped during the Sochi 2014 Paralympic Games, adding that it planned to reanalyse every Russian sample given at the event
The IPC allowed the Russian Paralympic Committee to present its case before it decided on the ban.
The IOC was widely criticised for ignoring the World Anti-Doping Agency (Wada) recommendation to ban Russia from the Rio Olympics.
Instead, each individual sporting federation was given the power to decide if Russian competitors were clean to compete.
A three-person IOC panel then had the final say.
In the end, more than 270 Russian athletes were cleared to compete at the Olympics.
Russia has filed its appeal to the Court of Arbitration for Sport against a total ban from the Rio Paralympics.