Two small bombs—tin pots filled with explosives—exploded harmlessly in an empty car parking area inside the Bangladesh Secretariat building that houses the government ministries in central Dhaka, senior police officer Nurul Islam said.
He said at least 10 more similar small bombs went off in other parts of the city, causing no injuries. Islam provided no details, and it was unclear who had set off the bombs.
The main opposition Bangladesh Nationalist Party is leading the nationwide strike Sunday and Monday, demanding the government find the party's organizing secretary, Elias Ali, who went missing two weeks ago.
The opposition blames the government and security agencies for Ali's disappearance, but authorities deny it. A rights group says at least 22 people, mostly politicians, have disappeared this year in Bangladesh.
Islam said police briefly detained six opposition activists, including the Bangladesh Nationalist Party's Publicity Secretary Rizvi Ahmed, as they tried to lead a march in central Dhaka.
The strike halted traffic and shut down stores and schools in the capital and across most of the country's 64 district towns, private TV stations ATN Bangla and Somoy TV reported.
In Dhaka, strikers smashed about a dozen vehicles that tried to defy the shutdown, police and witnesses said.
General strike is a common opposition tactic in Bangladesh to embarrass the government.
Last week, the opposition enforced three days of general strikes calling for Ali to be found.
Ali's disappearance has further complicated Bangladesh's fragile parliamentary democracy, already marred by a history of military coups since its independence from Pakistan in 1971.