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.
Immediately after the verdict, authorities shut down Facebook, Viber and WhatsApp aimed at preventing Jamaat supporters mobilising to protest against the ruling.
"We have taken steps to suspend the apps based internet services following the request from law enforcement agencies for security reasons," a Bangladesh Telecommunications Regulatory Commission spokesman said.
Internet services were also suspended for over an hour.
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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.
Today's verdict had cleared the way for their execution and they were now left with the last option of seeking presidential clemency.
Bangladesh had overnight stepped up nationwide security amid fears of clashes after the verdict.