A.T.M. Azharul Islam, 62, assistant secretary general of the Jamaat-e-Islami party, was found guilty of five out of six charges including the murder of hundreds of minority Hindus, rape, abduction and torture, prosecutors said.
As the verdict was delivered, Islam stood up in the dock and shouted that his conviction had been “dictated” by the government.
Defense lawyer Tajul Islam rejected the charges and said he would lodge an appeal.
Prime Minister Sheikh Hasina in 2010 opened an inquiry into war crimes committed during the nine-month war.
The tribunals have angered Islamists who call them a politically motivated attempt by Hasina to persecute the leadership of Jamaat-e-Islami, a key part of the opposition coalition.
More than 200 people have been killed in violent protests against the tribunal and its decisions, most of them Islamist party activists and members of the security forces.
Jamaat called for nationwide strikes on Wednesday and Thursday to protest against the verdict.
Bangladesh became part of Pakistan at the end of British rule in 1947 but broke away in 1971 after a war between Bangladeshi nationalists, backed by India, and Pakistani forces.
About 3 million people were killed, according to official figures, and thousands of women were raped.
The tribunal has convicted 16 people, most of them Jamaat leaders, and sentenced 14 of them to death. One Islamist politician was executed in December 2013.
International human rights groups have said the tribunal falls short of international standards. The government dismissed that criticism.
Some factions in Bangladesh, including the Jamaat, opposed the break with Pakistan, but the party denies accusations that its leaders committed atrocities. -Reuters