"This is a very, very important issue. You both (the Centre and state government) sit together and try to find a solution to the contentious issue," a bench comprising Chief Justice J S Khehar and Justices D Y Chandrachud and S K Kaul said.
The court asked them to file a proposal on the issue within four weeks.
It was also stated that Sikhs, who fell under the minority category nationally, are in majority in Punjab.
"Let us focus on Jammu and Kashmir. Let us deal with the issue at hand," the bench said.
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Senior advocate Gopal Subramaniam, representing Jammu and Kashmir, said that the state government is willing to sit and try to find a solution to the issue.
Taking note of willingness of both the governments, the bench said, "We hope and expect that a fruitful decision will emerge on the next date of hearing."
The plea also alleged that rights of religious and linguistic 'minorities' in the state were being "siphoned off illegally and arbitrarily" due to extension of benefits to "unqualified sections" of the population.
Sharma alleged the provisions of the National Commission for Minorities Act is not applicable in Jammu and Kashmir due to caveat put by Article 370 of the Constitution and moreover, crores of rupees are being given to members of the majority community under various schemes meant for linguistic and religious minorities.
on the Centre for not filing its reply to the PIL alleging that minority benefits are being enjoyed by majority Muslims in Jammu and Kashmir.
It has been settled that the identification of minority communities has to be decided as per the population data of the state in question, Sharma had said.
The apex court, however, had refused to restrain authorities from disbursing benefits to any community in the state.
The PIL has also sought the setting up of State Minority Commission for identification of minorities.
"The population of Muslims in Jammu and Kashmir according to the 2011 Census is 68.31 per cent. Communities which are eligible to be notified as minorities, were not awarded their due share of scholarship owing to their non-identification as minorities, thereby jeopardising their constitutionally guaranteed rights enshrined under Part III of the Constitution of India.
The plea also sought directions to consider extension of National Commission for Minorities (NCM) Act, 1992 to Jammu and Kashmir and make amendments so that benefits available to minorities of other states could also be given to the minorities of J&K.
"Appoint a committee of experts functioning under the direct supervision of this court to submit a comprehensive report identifying communities of the state of Jammu and Kashmir which qualify as religious and linguistic minorities," the PIL said.