At least a dozen people were reported injured in clashes between police and Islamist demonstrators in Bangladesh on Sunday, the third day of protests against the visit of India's Hindu-nationalist leader.

Five people died on Friday, and another six the next day, after police shot at demonstrators in several major districts across the Muslim-majority nation of 168 million people.

The protesters -- mostly from the hardline Islamist group Hefazat-e-Islam -- were angry at the visit of Indian Prime Minister Narendra Modi as Bangladesh marked 50 years of independence, accusing him of stoking communal violence against Muslims in his country.

At one new protest in Narayanganj just outside the capital Dhaka, Hefazat supporters chanted "action, action, direct action" as they blocked the key highway linking Dhaka with the port city of Chittagong.

Hundreds of demonstrators burnt furniture and tyres on the roads as they chanted anti-Modi slogans and called on authorities to investigate the shootings.

Police fired tear gas and rubber bullets after the protesters barricaded parts of the highway. A police spokesman told AFP they had since left the road.

Prothom Alo, the country's biggest Bengali-language daily, said at least 15 people were injured in the Narayanganj clashes.

Hefazat spokesman Jakaria Noman Foyezi told AFP thousands of its supporters joined demonstrations at its headquarters at Hathazari outside Chittagong, which is home to a top Islamic seminary.

The Islamist group has a nationwide network, and it has held large protests in the past demanding that Bangladesh introduce blasphemy laws. 

Protests were also held in the northeastern city of Sylhet, the eastern district of Brahmanbaria and in Bosila, a Dhaka suburb, but there were no reports of violence, local media reported.

As Bangladesh celebrated independence, human rights groups criticised the government for what they described as growing authoritarianism, including forced disappearances and extrajudicial killings.

Other groups -- including students, leftists and other Islamist outfits -- had also staged protests against Modi's visit on Friday and Saturday.