The PML-N government has completed formalities to send the convicted militants to gallows on Tuesday. The executions, if carried out, will end a five-year moratorium imposed by Zardari.
"President has referred the case of two convicts to PM and desired to discuss the issue with PM," Farhatullah Babar told PTI.
He also said that the "president has neither stayed any execution nor ordered any." It is not clear as yet how Sharif will respond to the proposal by Zardari to discuss it.
A counter-terrorism court in Sindh province has issued 'black warrants' for the execution of two members of the banned Lashkar-e-Jhangvi, Attaullah alias Qasim and Muhammad Azam alias Sharif.
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The two men were convicted by a counter-terrorism court in July 2004 for killing a Shia doctor and are scheduled to be executed on Tuesday.
So far government was determined to go ahead despite threats from the Taliban to target the PML-N government if militants are hanged.
According to official figures, Pakistan has more than 7,000 prisoners on death row, one of the largest populations of prisoners facing execution in the world.