A division bench comprising Chief Justice D Y Chandrachud and Justice P K S Baghel passed the order on a Public Interest Litigation filed by NGO People's Union for Democratic Rights (PUDR) and fixed November 25 as the next date of hearing in the matter.
The court also asked the Centre and the Uttar Pradesh government to file their counter affidavits by the next date of hearing.
The High Court order comes two days after the Supreme Court rejected Koli's plea to recall the death sentence which was awarded to him by a special CBI court in February, 2009.
Koli, who worked as a domestic servant at the house of Noida-based businessman Moninder Singh Pandher, is facing the gallows for the murder of a 14-year-old girl Rimpa Haldar.
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Both Koli and Pandher had been awarded death sentence in the Rimpa Haldar case though the latter was acquitted later by the Allahabad High Court. Pandher, who had been held guilty by the trial court along with Koli in a number of other related cases also, was recently released on bail.
Following an outcry over alleged inept handling of the case by Uttar Pradesh police, the case was handed over to the CBI in January, 2007.
After his death sentence in the Rimpa Haldar case was upheld by the Allahabad High Court vide the very order whereby Pandher was acquitted, Koli's subsequent appeal before the Supreme Court was turned down while his mercy petition was rejected by the President.
However, on October 28, the Supreme Court dismissed the recall application, clearing the decks for execution of the death warrant.