A Bench comprising Justices Surya Kant and Raj Mohan Singh postponed the decision after it was brought to its notice that the Punjab government has filed a plea saying that the implementation of the court's earlier order to perform the last rites could lead a law and order problem.
However, the Punjab government's plea could not be listed and therefore for a consolidated hearing on the issue the Bench directed to place all the appeals together for hearing on next Monday, defence said.
Ashutosh's body has been kept in a freezer since January after he was declared clinically dead by doctors.
Meanwhile, appeal filed by DJJS, which challenged the High Court's December 1 order, said that the courts were not "competent" to distinguish between a 'naturally dead body' and a body in 'samadhi' (deep meditation).
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The DJJS also said in its petition that it has not pleaded before the court whether Ashutosh was dead or not and the court "had gone beyond the scope of the pleadings".
On the other hand, Bihar native Dalip Kumar Jha, who claims to be Ashutosh's son, has sought handing over the body.
Jha said that the December 1 order of the court, in which it said that Jha failed to produce "sufficient evidence" to prove that he was Ashutosh's son, was "erroneous".
Both the parties have also contended that the court did not give them "sufficient" time to file an appeal against the December 1 order.
It had also directed the government to oversee the compliance of the order.