Violence broke out in at least four places, with police firing tear gas to control crowds of mainly students of Islamic schools, or madrassas, who brought much of the nation to a standstill by blocking roads.
The parties, known as the Islamic Law Implementation Committee, called the strike to protest against the government's move to pass laws ensuring equal property and inheritance rights for women in the Muslim-majority country.
At Fatikchhari, near the southeastern port city of Chittagong, some 3,000 madrassa students attacked buses and burnt down a petrol station, local police chief Mohiuddin Selim told AFP.
"They smashed bus windows and beat passengers," said local police chief Mohiuddin Selim, adding police used tear gas, rubber bullets and fired live rounds into the sky to break up the protests.
Some 1,000 protesters blocked the main Dhaka-Chittagong highway 10 kilometres (six miles) south of Dhaka for three hours and fought police with sticks when they tried to remove them, local police chief Badrul Alam said.
More than a dozen police officers were injured across the country and at least 150 people were arrested, police said.
"Up to 1,500 protesters suddenly attacked us with stones and bamboo sticks. They torched one of our lorries," inspector Shahidul Haq of central Nagarkanda town told AFP.
Most shops, businesses and schools in Dhaka were shut and major roads in and around the capital were almost deserted. A senior Dhaka police officer said around 10,000 police had been deployed in the capital.
"Security is tight to prevent any violence," Dhaka police commissioner Benazir Ahmed said.
Small Islamic groups led by firebrand cleric and ex-lawmaker Mufti Fazlul Haque Amini have been staging sporadic protests since the government announced its plan on March 7, arguing that it goes against the Holy Quran.
Bangladesh, whose population is 90 percent Muslim, has a secular legal system but in matters related to inheritance and marriage Muslims follow sharia law, which enjoys popular support in conservative, rural areas.
Sharia as practised in Bangladesh's inheritance law generally stipulates that women inherit half of what her brother receives. Women's groups have long railed against the disparity and demanded equal rights.
Prime Minister Sheikh Hasina on Sunday said the government's proposed law was not against the Quran.
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