Supporters of an religious political party in Bangladesh have exploded homemade bombs and clashed with police during a general strike, leaving dozens injured, police and local media say.

The Jamaat-e-Islami party called a nationwide shutdown for Thursday, to back the party's demand that the government stop the trials of its leaders on charges of crimes against humanity involving Bangladesh's 1971 war of independence from Pakistan.

At least eight people were injured after stone-throwing protesters clashed with baton-wielding police in Jessore district, about 135km west of the capital, Dhaka, the Daily Star newspaper reported.

The Somoy TV and Independent Television stations reported that Jamaat members exploded crude bombs and attacked vehicles to enforce the strike. Several people were injured in the violence in Dhaka, the reports said.

Six leaders of the party, including its chief Matiur Rahman Nizami, are on trial before Dhaka's International Crimes Tribunal.

They are accused of playing roles in atrocities carried out by Pakistani troops during the nine-month conflict.

The Jamaat denies the charges, although it did oppose Bangladesh's separation from Pakistan. The war killed three million people, and 200,000 women were raped, according to the Bangladeshi government's figures.

Early this month, fugitive Islamic cleric Abul Kalam Azad was sentenced to death in the first verdict in the war crimes trial.

International rights groups have called for fair trials to be held in accordance with international standards.