Justice P.S. Teji asked the Delhi Police to respond on the pleas before the next date of hearing on August 9.
There are two petitions seeking cancellation of Kanhaiya Kumar's bail.
One petition sought direction for initiation of perjury proceedings against the Jawaharlal Nehru University Students Union (JNUSU) president for allegedly filing a false affidavit to obtain bail.
Advocate R.P. Luthra, one of the petitioners, sought cancellation of the bail on the ground that his speeches subsequent to his release were "anti-national" which violated the bail conditions.
The plea said Kanhaiya Kumar had violated the conditions imposed on him by the Delhi High Court when it granted him bail on March 2.
The court had said that Kanhaiya Kumar will "not participate actively or passively in any activity which may be termed as anti-national".
Kanhaiya Kumar was arrested on sedition charge after taking part in a controversial February 9 event held in the JNU campus on Kashmir.
"Kanhaiya Kumar continued his anti-national activities on each and every day and it became unbearable when he alleged in public that the Indian armed forces rape women in Kashmir," the pleas said.
The petitioners urged the court to cancel the bail given to Kanhaiya Kumar at the earliest "to minimise future damage to the reputation of India".
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