Lawyers of Jamaat-e-Islami leader Muhammad Quamaruzzaman filed the petition with the appellate division of the Supreme Court on the last day of the stipulated 15-day period since receiving the written court verdict, in the hope their client "would get justice in the review process".
"In his prayer Mr Quamaruzzaman sought cancellation of the verdict and acquittal of the (war crimes) charges," defence lawyer Shishir Manir said.
The 63-year-old convict's lawyers filed the review petition a day after holding a meeting with Quamaruzzaman, senior assistant secretary general of the fundamentalist Jamaat, which opposed Bangladesh's independence during the 1971 liberation war against Pakistan.
Bangladesh is trying high-profile suspects and alleged 1971 war criminals in the country's International Crimes Tribunal under a special law which also allows the convicts to seek presidential mercy in their last ditch efforts to evade capital punishment.
But Quamaruzzaman's lawyers said he would decide whether he will seek presidential mercy after consulting his lawyers if his review petition is also rejected.
Prison authorities earlier read the death warrant out to him on February 19, the day the tribunal issued it soon after the apex court validated its original 2013 judgement sentencing him to death for committing crimes against humanity during the war.
Jail authorities earlier said they were ready to carry out the sentence so the execution procedure could be completed immediately if his review petition was rejected.
Quamaruzzaman was found him guilty of mass killing, murder, abduction, torture, rape, persecution and abetting torture in central Mymensingh region.