Lawyers of Nizami, president of the Bangladesh Jamaat-e-Islami party, submitted the review petition on behalf of their client, who is now in a prison in Kashimpur on the outskirts of capital Dhaka, Xinhua reported.
If his review petition is rejected, the last option for him will be to seek presidential mercy.
Bangladesh's Supreme Court on January 6 upheld the death penalty for the 73-year-old Motiur Rahman Nizami over war crimes during the country's war of independence 45 years ago.
Bangladesh's International Crimes Tribunal-1 issued Nizami's death warrant on March 16 hours after the country's apex court released its full verdict.
Nizami served as agriculture and industries minister in the then Prime Minister Khaleda Zia's 2001-2006 cabinet.
The apex court upheld capital penalty for the Islamist party chief on three charges and life imprisonment on two charges.
On October 29, 2014, the International Court of Terrorism handed down capital punishment to Nizami for war crimes which include mass killings of Bangali intellectuals.
Nizami was indicted in 2012 with 16 charges of crimes during the 1971 war.
Nizami's party had earlier claimed that the government filed ill-motivated, baseless cases against its top leaders in order to make the party leaderless.
Nizami is among the top Jamaat leaders who have been tried in two war crimes tribunals which Prime Minister Sheikh Hasina's Bangladesh Awami League-led government formed in 2010 to bring the perpetrators of 1971 war crimes to book.
Three Jamaat leaders -- Abdul Quader Molla, Muhammad Kamaruzzaman and Ali Ahsan Mohammad Mujahid -- have been executed.
Besides, Jamaat secretary general Ali Ahsan Mohammad Mujahid and opposition Bangladesh Nationalist Party (BNP) leader Salaudin Quader Chowdhury were executed on November 22 last year.
Both the BNP and Jamaat have dismissed the court as a government "show trial", saying it is a domestic set-up without the oversight or involvement of the UN.
Muslim-majority Bangladesh was part of Pakistan and called East Pakistan till 1971. The government of Hasina said about three million people were killed in the Bangladesh Liberation War in 1971. (IANS)