A war crimes tribunal pronounced the sentence after convicting Delwar Hossain Sayedee of atrocities, including rape and mass killings, during the country's war of independence from Pakistan in 1971, the Voice of America reported.
Sayedee, a senior member of the Jemaat-e-Islami party, is the third member of the party sentenced to death for war crimes since 2010.
During the three days of protest since the sentence was handed down, at least 40 people have been killed.
On Saturday, hundreds of student activists clashed with police in the port city of Chittagong when police tried to remove barricades set up by the protesters, the BBC reported.
Police said they fired live ammunition and rubber bullets at the protesters, who attacked them with sticks and stones.
A total of nine Jamaat leaders and two members of the opposition Bangladesh Nationalist Party are being tried.
Human rights groups have questioned the fairness of the trials, contending that members of the defense have been pressured.
The government has denied allegations the trials are politically motivated.