The strike, which began at dawn on Saturday and was set to end on Monday evening, drove most transport off the streets of the crowded capital and closed shops and schools.
Witnesses said police used batons to disperse hundreds of opposition activists marching on Dhaka streets at sunrise and detained at least 10.
Police put up barbed-wire barricades outside the central office of the main opposition party, the Awami League, in Dhaka's Gulistan Square and chased off groups of chanting protesters, witnesses said.
The Awami League, strongest of the opposition parties, called the marathon countrywide strike after an explosion at a rally in the country's northeast killed a senior party leader and four other people on Thursday.
Police said the explosion, which wounded about 70, was caused by a grenade thrown by an unknown assailant. The stoppage is likely to largely paralyse business as well as activities at the country's main port, Chittagong, officials and trade unions said.
Thursday's blast killed a senior
party leader and four others
"We are facing a complete shutdown," said a resident of Cox's Bazar, a sea resort in the southeast. "Streets are empty, a few tourists have ventured to the beach on foot but there are no shops open," he said.
Thursday's blast - the latest in a series to rock the country over the past year - killed former UN official, diplomat and finance minister Shah Abu Muhammad Shamsul Kibria, 73, a key Awami leader, as well as his nephew and three others.
Prime Minister Begum Khaleda Zia condemned Kibria's death and vowed to bring his killers to justice. But Awami chief Shaikha Hasina, who herself narrowly escaped injury in a grenade attack at a rally in Dhaka last August, and other opposition leaders complained.
"This government has failed to conduct any independent and full investigation into any of the past bombings. Instead they
have tried to protect the perpetrators. So we don't expect
anything different from them now," she said late on Friday.
Envoys of European Union countries met Kibria's wife, Asma Kibria, at her home on Friday evening to convey their sympathies.
On behalf of the group, British High Commissioner Anwar Choudhury later said: "We are deeply concerned that the apparent failure to properly investigate previous similar attacks has led to a climate of impunity which encourages a continuation of such incidents."
Choudhury, who himself was wounded in a bomb attack while visiting a Muslim shrine in northeast Bangladesh last May, called upon the government "to ensure the due process of law through proper investigation".