A last-minute appeal to the Bangladesh Supreme Court led to a temporary reprieve from the execution scheduled for Wednesday, but the court dismissed the appeal and affirmed the death sentence.
Human rights experts from the United Nations, which opposes the death penalty, had urged the execution be halted, citing concerns about whether Mollah, 65, had received a fair trial, CNN reported.
A five-judge bench headed by Chief Justice Mohammed Muzammel Hossain dismissed Mollah's petition and upheld the death sentence following a lengthy hearing Thursday, the Bangladesh Sangbad Sangstha news agency reported.
Mollah, former assistant secretary-general of the now-banned Jamaat-e-Islami party, was accused of genocide in heading the al-Badr militia during Bangladesh's 1971 war of independence from Pakistan. He was accused of having a role in the slaughter of 344 people, including women and children, in the Dhaka suburb of Mirpur.
He denied the charges, but was convicted on six charges of war crimes and crimes against humanity in 2013.
He was previously given a life sentence but the Supreme Court changed it to death in September after saying the charges against him were proved beyond doubt.
The life sentence given the "Butcher of Mirpur" sparked demonstrations by tens of thousands of people who deemed the sentence too light, the Bangladeshi online newspaper bdnews24.com reported Thursday.
Besides Mollah, a tribunal set up by the Bangladeshi government to look into the events of 1971, has convicted several other Jamaat leaders. This has led to widespread protests, aggravating the current political tensions between the government and several opposition parties. Jamaat supporters say the tribunal trials are politically inspired.
The 1971 independence war from which Bangladesh emerged as an independent country resulted in the deaths of hundreds of thousands of people and left deep scars in the minds of Bangladeshis. Mollah was accused of being part of a group that did not want to split from Pakistan and aided the Pakistani military's crackdown.
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