A division bench headed by Chief Justice Satish Chandra Sharma granted four weeks to the Centre for filing a detailed response in the matter.
The last date of registration was August 3.
The Railway Minister told the House that 'Police' and 'Public Order' are state subjects under the Seventh Schedule to the Constitution of India.
In another development, the Supreme Court on Tuesday transferred all the writ petitions challenging the Agnipath scheme for the armed forces before it to the Delhi High Court, where a similar challenge against the scheme is already pending.
Youth are keen to join the Armed Forces under Agnipath scheme and Air Force in particular.
These include a plea by armed forces aspirants seeking an urgent hearing in the matter stating the scheme should not be made applicable to those who are already undergoing the selection process.
The online registration process for Indian Air Force under the Agnipath scheme started on June 24 and concluded on July 5.
A counsel mentioned the petition before a vacation bench comprising Justices Indira Banerjee and J.K. Maheshwari.
The first batch of Agniveervayu would be enrolled by December and training would commence by December 30.
On the heels of widespread protests by opposition political parties demanding a rollback of the Agnipath scheme, the Indian Metal And Ferro Alloys (IMFA) Limited has decided to give the young Agniveers a chance to work for them after completion of their tenure with defence forces.
Minister of State Tusharkanti Behera on Tuesday termed the scheme as brilliant. The development came amid speculation that BJD will extend its support to the Presidential candidate selected by NDA.
The plea has sought directions to the Centre and the Uttar Pradesh, Telangana, Bihar, Haryana and Rajasthan governments to submit a status report on the violent protests.
PM Modi maintained that the double engine government of the BJP is constantly working towards ease of living as well as ease of doing business. "Private sector is also involved in building nations and I thank them," he underlined.
The merits of having a young armed force and a cost-effective Armed Force have been deliberated for years and finally Agniveers have emerged.
Of the 529 trains, 181 were mail/express trains and 348 were passenger trains.