In the Mahakhali area of Dhaka, police baton-charged about 150 anti-government protesters calling for electoral reform, a police spokesman said. He said the demonstrators had thrown stones at officers.
Elsewhere in the capital and in nearby Narayanganj and northern Sirajganj, 60 people were reported injured in battles with police who used tear gas and rubber bullets.
Shops, private offices, schools and colleges were closed throughout Bangladesh, officials said.
The 36-hour national strike, which began at dawn on Tuesday, follows a protest in Dhaka on Sunday.
It is the latest in a series of demonstrations by an alliance of 14 opposition parties led by the Awami League, the largest.
About 10,000 police and paramilitary Bangladesh Rifles troopers were in the capital, its chief of police said.
Mizanur Rahman said: "Inter-district [transport] has been snapped for buses and trucks and the city streets are empty."
In southeastern Chittagong, the country's second-biggest city, 3,500 extra police were deployed and deliveries from the port were suspended.
The Awami League has threatened to call indefinite strikes and boycott the next parliamentary election, scheduled for January, if its demands for electoral reforms are not met.
Abdul Jalil , the party's general-secretary, said: "We will never allow the election to be held unless the existing electoral system is reformed and the chief election commissioner and his two deputies are removed."
The party accuses the three officials of being pro-government.
It also wants officials in the caretaker government, which oversees the elections, to be appointed with the consent of all political parties.
The present system under which the officials are selected by the outgoing government could lead to electoral manipulation, according to the Awami League.
The Bangladesh Nationalist Party of Khaleda Zia, the prime minister, leads a four-party Islamist-allied coalition government. The caretaker government is due to take over in October.