The procedure adopted for electing four representatives as life members on March 4, and the April 6 NRAI polls, had been challenged by Athens Olympic silver medallist Rajyavardhan Singh Rathore.
Taking note of Rathore's plea, the court had said that denying him the right to contest elections was not justified, which prompted the NRAI to take legal discourse.
"The association today filed an appeal to the double bench -- it was a single bench earlier -- of the Delhi High Court," an NRAI official told PTI.
The court gave the sports body the liberty to hold fresh elections in accordance with law.
"No election which has been held after depriving the persons desirous of contesting the chance to contest can be held to be a valid election and cannot be given any recognition," Justice P K Bhasin had said in that ruling.