Home Minister Asaduzzman Khan Kamal said the execution of fundamentalist Jamaat-e-Islami Secretary General Ali Ahsan Mohammad Mujahid and BNP leader Salahuddin Quader Chowdhury, was now only a "matter of time".
"They could be executed anytime on completion of necessary procedures," he told reporters on the sidelines of a function.
67-year-old Mujahid and 66-year-old Chowdhury could seek a presidential pardon as per their "constitutional right" but so far they have not opted for it.
A prison official, on condition of anonymity, said preparedness for the execution of the two leaders has been "completed (and) we are discharging our responsibilities as per law and conventions."
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Jail authorities last night had read out the written text of the Supreme Court order to the death row convicts.
Supreme Court's Appellate Division issued the full text of the final verdict yesterday, a day after it rejected the review petitions of Mujahid and Chowdhury, paving the way for their execution.
Close relatives of Mujaheed and Chowdhury met them yesterday at Dhaka Central Jail two days after they were transferred to the facility from the suburban high security Kashimpur Central Jail.
Talking to reporters after meeting Mujahid, his son Ali Ahsan Mabru yesterday told reporters that his father would "send a special prayer to the president, but it will not be a mercy petition."
Meanwhile, there was a nationwide security vigil in Bangladesh amid fears of a backlash over the execution with the government saying plots were being hatched to thwart the war crimes trial.
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.
None of them had sought the presidential clemency.