Besides the convict, his juvenile son also allegedly took part in the offence of rape and murder of the minor.
Issuing notice the Rajasthan government, a bench of justices J S Kehar and C Nagappan said, "The execution of death penalty shall remain stayed."
Earlier, the apex court had agreed to hear the appeal of the condemned prisoner Kalu Khan during the vacation period.
The girl, whose parents had gone out, was lured by the convict on the promise of giving her some berries on the morning of May 3, 2012, the prosecution had said.
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Khan and his minor son raped the victim and later, as her condition worsened, they killed her before burying her in a pit in their courtyard, it had said.
In the appeal, filed through lawyer Asha Jain Madan, the convict said that the courts below have failed to "appreciate that the entire prosecution case rests solely on circumstantial evidence which is wholly insufficient to base the conviction of the petitioner and that too for award of capital sentence".
It submitted that the prosecution's story is "totally improbable" as the convict and his minor son could not have done the "sinful" act together.