Authorities have denied the allegations.
Asif Munier, son of a university teacher who was killed in 1971 for supporting independence, said he was happy with the decision.
“Yes, we are happy because justice has been served. ... It's not about any revenge but for justice,” Munier told The Associated Press immediately after the decision came from the Supreme Court.
Carrying out the execution would complicate an already critical political situation in Bangladesh, where the opposition has carried out violent protests for weeks to back a demand for an independent caretaker government to oversee the general elections set for Jan. 5.
The government has rejected that demand and said a political government headed by Hasina would conduct the elections, although the opposition alliance led by former Prime Minister Khaleda Zia plans to boycott the vote.
Weeks of blockades and general strikes have left nearly 100 people dead since October.
Mollah was found guilty by the special tribunal in February of killing a student and a family of 11 and of aiding Pakistani troops in killing 369 others during the independence war.
He was sentenced to life in prison, but the Supreme Court changed that to a death sentence in September.
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