The four-member bench led by Chief Justice Surendra Kumar Sinha rejected the final review petitions of Jamaat-e-Islami Secretary General Ali Ahsan Mohammad Mujahid and Bangladesh Nationalist Party (BNP) leader Salahuddin Quader Chowdhury.
Mujahid, 67, and Chowdhury, 66, were senior ministers in ex-prime minister Khaleda Zia's BNP-led coalition government with the fundamentalist Jamaat being its key partner.
Mujahid, the second most senior member of Jamaat, was found to be a key mastermind of the massacre of the country's top intelligentsia just ahead of the December 16, 1971 independence war victory.
Bangladesh's International Crimes Tribunal had handed down death sentences to them in separate cases of crimes against humanity in 2013 and the apex court upheld the death penalty to Mujahid in June and to Chowdhury in July this year.
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Immediately after the apex court verdict, authorities fearing violence by supporters of two opposition leaders shut down Facebook, Viber and WhatsApp aimed at preventing Jamaat supporters mobilising to protest against the ruling.
"We directed the operators to temporarily shut the access to online messaging and calling applications including the Facebook in line with requests of security agencies," a spokesman of Bangladesh Telecommunication Regulatory Authority told PTI.
"But we just issued another directive asking for blocking eight other online communication services for public security," the spokesman added.
Operators said the internet service was also stopped for over an hour for technical reasons but the BTRC spokesman said no ban was issued to block the internet and mail services.
BNP did not react to the verdict on Chowdhury but some reports said police chased away a few Jamaat activists in parts of the capital as they tried to stage street protests.
During the previous such judgments against several of their leaders, Jamaat spearheaded a violent campaign leaving dozens of people dead last year in their strongholds.