Zahid Hossain Khokon, a main opposition party official, was found guilty of 10 charges including forcibly converting minority Hindus to Islam during the nine-month war.
"He got the death sentence for six charges and 40 years' jail for four other charges," prosecutor Mukhlesur Rahman told reporters after the verdict was handed down.
Khokon, mayor of Nagarkanda town, disappeared after he was charged last year, and the court "ordered the national police chief and the district police chief to find and arrest him," he said. But Rahman said he believed the 70-year-old had fled to Sweden where he was hiding out with relatives.
Khokon is the second official from the main opposition Bangladesh Nationalist Party (BNP) to be handed the death penalty for war crimes.
The centre-right party has called the court's trials politically motivated, aimed at eliminating opposition leaders rather than rendering justice.
During the war, Khokon was an official of the party, whose members have also been tried and sentenced to death by the court.
Those convictions triggered the country's deadliest political violence since independence last year, when thousands of party activists clashed with police in protests that left some 500 people dead.
Prosecutors said Khokon led a militia in his home town that opposed Bangladesh's independence.
"He was directly involved in the killing of some 50 people. He forced Hindus to become Muslims and raped and tortured women," Rahman told AFP ahead of the verdict.
After Bangladesh gained independence, the Jamaat-e-Islami party was banned, so Khokon joined its now key ally the BNP.
One of BNP's top decision makers was also sentenced to hang last year for similar charges.
Defence lawyer Abdus Sukur Khan, who was appointed by the state for the trial, said Khokon did not receive justice.
Rights groups have said the trials fall short of international standards and lack any foreign oversight.
The government of Prime Minister Sheikh Hasina maintains the hearings are needed to heal the wounds of the conflict, which it says left three million people dead.
Independent researchers estimate that between 300,000 and 500,000 people died in the 1971 war.
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