Shivu Munishetti and Jadeswamy Rangashetti, whose mercy pleas had been rejected by the President early this month, had moved the apex court saying there was a delay of six years in deciding their clemency petitions.
The duo had been sentenced to death for brutally raping and murdering a teenaged girl in 2001.
Appearing for the convicts, senior advocate K V Vishwanathan sought stay on the execution of their sentence citing delay by the government in deciding their mercy pleas.
"It is asserted that in both the matters the mercy petition filed by the petitioners remained pending for six years. Since the connected petitions are pending before this Court, we are inclined to issue notice," the bench said.
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"Issue notice. In the meantime, there shall be an order of stay restraining the respondents from executing the sentence of death on the petitioners pursuant to the rejection of their mercy petitions by the President of India," it said and posted the matter for hearing after four weeks.
Shivu slashed his private parts and a hand with a blade, prison officials said. He was being treated in the jail and might be shifted to a district hospital, they said.
Shivu and Jadeswamy were arrested by Chamarajnagar police in connection with rape and murder of an 18-year-old girl on October 15, 2001.
The two were sentenced to death by a trial court in July 2005. The Karnataka High Court rejected their appeal and confirmed their death penalty in October 2005. The Supreme Court had upheld the High Court verdict in 2007.