The Supreme Court asked the central government on Monday for a detailed reply on the issue of deporting the Rohingyas to Myanmar.
The Rohingya are originally from Myanmar.
There are some 40,000 Rohingya registered with the UNHCR as living in India.
The government has been threatening to deport all of them.
The Rohingya however are reviled back home in Myanmar, with the Myanmarese seeing them as illegal immigrants from Bangladesh
There have been allegations of the Myanmarese army and paramilitary forces carrying out a "genocide" or "pogrom"against them in the western Myanmar state of Rakhine.
As bodies wash up, UN says 27,000 Rohingya have fled Myanmar
The petition against their deportation was filed with the Supreme Court by two Rohingyas -- Mohammad Sallimullah and Mohammad Shakir.
On Monday, they told the Supreme Court they would face certain death should they be deported to Myanmar.
In the last hearing, ANI reported their advocate Prashant Bhushan as asserting that such a move -- their deportation -- would be unconstitutional as the apex court had repeatedly ruled, as in the case of Chakma refugees, that it was the cardinal duty of the Union government to protect refugees who leave their own country because of persecution at the hands of state authorities.