Mir Quasem Ali, 64, a business tycoon and financier of Jamaat-e-Islami party, was sentenced to death in 2014 by the Bangladesh International Crimes Tribunal (ICT) for committing crimes against humanity.
The decision was confirmed by the Appellate Division of the Supreme Court in March 2016.
The experts' request comes as the Supreme Court prepared to review Ali's death penalty today.
"In light of its irreversibility, every measure must be taken to ensure that all the defendants before the International Crimes Tribunal, including the Appellate Division, have received a fair trial," it said.
The experts recalled that the Working Group on Arbitrary Detention found in 2012 that Ali's deprivation of liberty was arbitrary and in breach of provisions of the Universal Declaration of Human Rights and the International Covenant on Civil and Political Rights.
The UN human rights experts also expressed alarm at reports that Ali's son and part of his legal defence team, Mir Ahmed Bin Quasem, was abducted from his home earlier this month by Bangladeshi security forces, two weeks before his father review hearing.
"We understand that no information has been given on where he is being held, by whom or under what suspicion or charge. We urge the authorities to immediately disclose the whereabouts of Quasem," they said.
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