Bangladesh's International Crimes Tribunal (ICT-BD) in the capital also awarded "imprisonment until death" to a fifth war criminal for carrying out atrocities in northern Kishorganj.
The five were found responsible for abductions, torture and killings to help Pakistan to abort Bangladesh's birth in 1971.
All the convicts were former members of Razakar Bahini, a Bengali-manned auxiliary force of the Pakistan army in 1971.
Gazi Abdul Mannan, 88, said to be a commander of Razakar camp, Nasiruddin Ahmed, 62, his brother Shamsuddin Ahmed, 60, and Hafiz Uddin, 66, have been given death, while Azharul Islam, 60, has been given imprisonment until death.
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Only one of them, Shamsuddin, faced the trial in person while the rest, including a former Bengali captain of the Pakistani force, were tried in absentia.
Witnesses said the three-member special tribunal led by Justice Anwarul Haque sentenced one of the fugitives the imprisonment until death.
The verdict came as Bangladesh Supreme Court said it will pronounce the final verdict on May 5 on the death sentence it handed down to chief of fundamentalist Jamaat-e-Islami, Motiur Rahman Nizami, deciding his fate over crimes against humanity during the 1971 Liberation War.
Bangladesh has so far executed four war crimes convicts since the process began to try the top Bengali perpetrators of 1971 atrocities in line with the electoral commitment of Prime Minister Sheikh Hasina in 2008.
They subsequently died in the prison cells of a specialised state-run hospital due to old age ailments.