The PIL has been filed by advocate and BJP leader Ashwini Kumar Upadhyay.
Earlier the Supreme Court on June 7 refused to entertain a plea seeking a probe by the Central Bureau of Investigation into the Mathura violence.
The vacation bench comprising Justices P C Ghose and Amitava Roy directed Upadhyay to approach the High Court instead.
Read More: Mathura on edge as violence claims 24 lives
Last week violent scenes were witnessed in Mathura after the police attempted to clear a sect which had encroached upon some land at Jawahar Bag area of the temple town.
The members of the sect fired upon the police and killed two. In all 29 persons had died in the violent clash. 368 people have been arrested in connection with the Mathura violence.