A division bench comprising Justices Krishan Murari and Akhilesh Chandra Sharma posted the matter for further hearing on July 31.
"Some preliminary objections were today raised before the court with regard to maintainability of the petition.
"We will reply to these when hearing resumes on Monday", counsel for the petitioners S F A Naqvi said.
The petition has been filed by Gorakhpur resident Parvez Parwaz, who had also filed an FIR in connection with the riots, and one of the witnesses in the case Asad Hayat.
"The state government also raised some objections about the credentials of the petitioners, highlighting some criminal cases against Parwaz and different contact addresses given by Hayat on two different occasions", he said.
Yogi Adityanath, who heads the sprawling Gorakhnath temple besides having been a five-time BJP MP from Gorakhpur, has been named in the FIR alongside the then city Mayor Anju Chaudhary and local MLA Radha Mohan Das Agarwal.