The four-member bench of the appellate division of the court will decide the fate of Jamaat-e-Islami secretary general Ali Ahsan Mohammad Mujahid and opposition Bangladesh Nationalist Party leader Salahuddin Quader Chowdhury.
The bench led by Chief Justice Surendra Kumar Sinha also passed an order rejecting an additional prayer by Chowdhury seeking to get testified eight foreigners including five Pakistanis in his favour during the review hearing.
"The court rejected his prayer (for testifying) the foreign nationals)," attorney general Mahbubey Alam said.
Several lawyers said the review process was unlikely to take a longer time as the court earlier took only a day to hear and reject review petitions of condemned war criminals Jamaat assistant secretaries general Abdul Quader Molla and Mohammad Kamaruzzaman, who were eventually hanged.
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Both Mujahid and Chowdhury are in their late 60s and were senior ministers in ex-prime minister Khaleda Zia's BNP-led coalition government with Jamaat being its key partner.
Mujahid was found to be a key mastermind of the massacre of the country's top intelligentsia just ahead of the December 16, 1971 victory. Chowdhury carried out atrocities particularly at his home district of southeastern Chittagong.
Authorities have tightened security across the country fearing violence. "We have intensified security across the country," a senior police officer told PTI.
Citing sources, private news portal BDNEWS24.Com said, "law enforcement and intelligence agency officials have claimed that they have concrete information on disruption to law and order centring the possible execution of two war criminals".
"Saturday's attacks on publishers may be a part of the plan...More such attacks may come in this month as the government moves ahead with the execution of the two big war criminals," it said, quoting an intelligence agency official.
On Saturday, a publisher was killed and another wounded along with two bloggers when machete wielding assailants attacked two publishing houses, an assault claimed by 'Ansar al Islam' also known as 'Ansarullah Bangla Team' or self-proclaimed Bangladesh branch of Al-Qaida.
Home Minister Asaduzzaman Khan Kamal had told PTI the Islamist outfit was ideologically linked to Jamaat, hinting that the orchestrated attacks were part of plans to destabilise Prime Minister Sheikh Hasina's government.