Police firing rubber bullets shot dead a protester on Monday in demonstrations in eastern Bangladesh as a strike called by the largest Islamist party paralysed life across the nation.

At least 14 people have been killed during protests against government trials of Jamaat-e-Islami party leaders for atrocities allegedly committed during the 1971 independence war from Pakistan.

The Jamaat-e-Islami declared the latest strike to protest against the death last Friday of four of its activists in police shooting in the southeastern city of Cox's Bazaar.

The new violence erupted in the town of Chouddogram, a day after parliament amended war crime laws to allow groups, not just individuals, to be prosecuted for war crimes.

It also amended the law to ensure the Jamaat leaders can be swiftly executed if convicted and the verdict challenged if the sentence is less than death.

Police said the man's death on Monday came when they fired rubber bullets at about 200 brick-hurling Islamist demonstrators.

"One Shibir (Jamaat student wing) activist died after being shot by a rubber bullet in the head," police constable Shahadat Hossain told AFP, adding two other protesters were injured in the police firing.

In the capital Dhaka, security was tight with the government deploying border guards in addition to over 10,000 policemen. Roads in Dhaka and inter-city highways were largely empty while many shops and offices were shut.

A young man was killed in the city after a bus lost control trying to evade bricks thrown by strikers, privately owned Independent TV reported.

The demonstrations and counter-demonstrations have intensified since a top Jamaat leader was sentenced to life imprisonment earlier this month for mass murder in the 1971 war -- a penalty judged too lenient by the demonstrators.

Late on Friday Ahmed Rajib Haider, a blogger who helped organise the anti-Islamist protests, was hacked to death with a machete near his Dhaka home.

Eight Jamaat leaders, including its chief and deputy chief, and two from the main opposition Bangladesh National Party are still on trial by the court for alleged atrocities in the war which government claimed three million lives.

Both parties say the trials by the government-appointed war tribunal are based on bogus charges and part of a political vendetta against the opposition.

The government rejects the accusations, saying the trials are needed to heal the wounds of the war. It accuses Jamaat leaders of being part of pro-Pakistani militias blamed for much of the 1971 carnage.