Fundamentalist Jamaat-e-Islami Secretary General Ali Ahsan Mohammad Mujahid and BNP leader Salahuddin Quader Chowdhury sought presidential clemency amid preparations for their execution, officials said.
"The jail authorities informed me that they have sought presidential clemency," Law Minister Anisul Huq told PTI.
Home Minister Asaduzzaman Khan also confirmed that his ministry received their petitions but did not elaborate further.
Officials familiar with the process said the petitions would now be sent to the Bangabhaban Prudential Palace through the law ministry.
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The officials declined to divulge the contents of the clemency petitions but legal experts said the convicts must "unconditionally admit" their guilt and "express remorse" for the crimes in their mercy petitions.
67-year-old Mujahid and 66-year-old Chowdhury are the first war crimes convicts to seek presidential clemency.
Previously, two war crimes convicts -- Jamaat leaders Abdul Kader Mollah and Mohammad Quamaruzzaman -- have been executed since Bangladesh in 2010 initiated the process to expose the Bengali-speaking collaborators of Pakistan Army for crimes against humanity during the 1971 Liberation War.
Attorney General Mahbubey Alam had earlier said the two convicts have exhausted all their legal options against their conviction but could seek the presidential clemency as part of their "constitutional rights".
State prosecutor Tureen Afroz said Bangladesh' Constitution empowers the President with the authority to grant clemency to any convict "but we hope the president will not exercise the power."
"Article 53 of the Vienna Convention restricted the scope to grant clemency to convicts of mass killing and crimes against humanity and the Rome Statute of the International Criminal Court also clearly stated in that no state or person pardon such criminals," she said.
The apex court judgement was immediately forwarded to Bangladesh's International Crimes Tribunal, which originally handed down the capital punishment to them in 2013.