The matter came up for hearing before a bench headed by Acting Chief Justice Gita Mittal, who recused herself and directed that IRF's appeal be listed before another bench.
The matter has now been listed before another bench on July 27.
While seeking setting aside of the ban imposed on it, the IRF in its plea has contended that the "tribunal erred in observing that there is material indicating communal riot because of the speech made by Naik".
The IRF sought setting aside of the May 11 verdict and said that the tribunal has wrongly decided the question on the liability of the organisation in view of the alleged action of Naik and his aide Arshi Qureshi.
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"It failed to appreciate that it was undisputed position that Naik is the president of the IRF, but the same could not reflect upon the action carried out by him in his individual capacity," the IRF's plea filed through advocate S Hari Haren said.
The tribunal, headed by Justice Sangita Dhingra Sehgal of Delhi High Court, had found that Naik has failed to take part in the legal proceedings before it and was "absconding and untraceable".
The tribunal on February 23 had ordered in-camera hearing in view of the confidential material being scrutinised by it.
Upholding the Centre's November 17, 2016 notification banning IRF for five years, the tribunal had said that there were sufficient reasons and cause to declare IRF an unlawful association.
IRF had moved the tribunal against the November 17, 2016 notification of the of the Ministry of Home Affairs imposing an immediate ban on the organisation under the Unlawful Activities Prevention Act.
However, since the tribunal declined to hear the matter before February 6, the foundation had moved the Delhi High Court challenging the immediate ban.
The Judicial Tribunal was set up to look into the ban on controversial preacher's NGO.
It had noted that Naik had failed to give clarification that the speeches had been made in his individual capacity and not on behalf of IRF.
"Even though IRF is not accused but there is material which shows that Naik was the founder of IRF and empowered to assign any work on behalf of IRF to others associated with IRF," it had noted.