Solicitor General Tushar Mehta representing the Centre submitted before the top court that not a single student has been arrested by police in the case connected with the agitation against Citizenship Amendment Act.
Violent protests had rocked the capital on Sunday against the CAA.
A bench headed by Chief Justice S.A. Bobde and Justices B.R. Gavai and Surya Kant said the High Court Chief Justices after hearing the Centre and state governments, would set up appropriate committee headed by retired top court or High Court judges to conduct probe into the alleged police excesses against students.
The apex court also declined to provide any protection from arrest to those who are found to be involved in the violent protests.
The court observed that it will be better if the aggrieved students move concerned High Courts falling under the jurisdiction of the respective incidents.
"Serious grievances have been raised by petitioners. We are sure that High Courts will look into matter after hearing both sides and appoint fact finding committee... Chief Justices of High Courts will respond adequately", said the Chief Justice.
Senior advocate Indira Jaising, representing a group of alumni from both Jamia Millia Islamia and AMU, said there should not be any coercive action against the student community.
"My petition seeks relief for the students... FIRs are being filed against students one after the other all over the country", said Jaising before the court.
She insisted that in order to get peace, police cannot file FIRs against thousands of students and throw them behind bars.
Chief Justice replied that you may be innocent, but what about if police thinks somebody has broken the law. "Somebody is throwing stones and somebody is damaging vehicles", said the Chief Justice.
Jaising insisted that it is the duty of the state to provide humanitarian aid to people who have received injuries. "This court had provided medical aid in earlier cases... Universities are shut down prior to the last day of the vacations and then they tell students to go home overnight, where would these students go", said Jaising.
She urged the court to constitute a committee having pan-India jurisdiction to examine incidents of violence breaking out in various parts of the country. The Chief Justice declined to entertain this request, instead said matters should be brought before the concerned High Courts.
Counsels representing students insisted that committee headed by retired judges of the apex court instils confidence in the people, and it will eventually help control violence.
( With inputs from IANS )