A rickshaw driver died after being hit with stones during a protest in southern Bangladesh by supporters of the country's largest party.

Elsewhere, brick-throwing demonstrators battled with police who retaliated with rubber bullets and tear gas, officers said.

The violence comes as towns and cities shut down after the Jamaat-e-Islami party called a nationwide strike to protest the death sentence handed on Tuesday to Abdul Quader Molla for crimes committed during the 1971 war of independence.

"The autorickshaw driver came under attack from Jamaat supporters at a place called Talerchar this morning. He was hit by several stones," said Anisur Rahman, police chief of the coastal district of Noakhali.

"He was rushed to a hospital at Companyganj in Noakhali where the doctors declared him dead," Rahman told.

The Supreme Court sentenced Molla to death, toughening the sentence originally handed down by the country's war crimes tribunal, and rejecting an appeal for acquital by his defence lawyers.

Molla, 65, the fourth-highest leader of Jamaat, had been given a life sentence in February by the International Crimes Tribunal. That sentence sparked deadly protests and riots by Islamists but also by secular activists on the other side who considered it too lenient.

The tribunal has since January convicted six Islamists of crimes related to the 1971 war, in which pro-independence fighters battled Pakistani forces which were helped by local leaders.