The division bench of Justices V M Kanade and Revati Mohite Dere, however, refused to pass any order.
"We shall not express any opinion on the issue but we appeal to religious leaders of the community to go into the matter," the judges said.
The court also allowed Muharram processions to be held as per the schedule on December 14.
Advocate General Sunil Manohar, on behalf of the state government, said the processions would be videographed. The state, he said, would not interfere but would step in only if serious injuries are caused to the children.
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Muharram marks the anniversary of the battle of Karbala in which Imam Hussein Ali, the grandson of Prophet Muhammad, was killed. To mourn his killing, participants hit themselves with sharp objects in keeping with the tradition.
Members of Shia sect thronged the court today to express their opposition to the PIL (which wants a ban on children's participation on the ground that they get injured during Matam). However, police stopped them from entering the courtroom.
Several members of the community have intervened in the petition. Their lawyers today argued that the court should dispose of the PIL as the petitioner was a Sunni Muslim and instead, they said, the court should take this up as suo motu (on its own) petition.
The petitioner Faizal Mohammed Benaraswala said he had received threats for filing the PIL.
The next hearing would be on January 13.