Hundreds more were wounded during the attack at an opposition political rally.
Witnesses said at least 25 people were injured in the clashes in the capital, Dhaka, on Tuesday and police picked up about 50 protesters.
Tuesday's violence erupted after police tried to stop hundreds of protesters from taking to the streets, witnesses said.
The protesters waved clenched fists in the air and shouted "Down with the government!"
About 100 others had been injured in similar clashes on the eve of the dawn-to-dusk strike, called by the main opposition Awami League party and backed by several leftist parties, the United News of Bangladesh news agency reported.
The protest shut down shops and schools and disrupted traffic across Bangladesh.
At least 20 people were killed and more than 300 injured when more than a dozen grenades were lobbed into the crowd while opposition leader Shaikha Hasina was speaking outside her Awami League headquarters on Saturday.
Mass protests and violence spread across Bangladesh to protest against the attack, putting security forces on high alert.
Many were also wounded
during Saturday's attack
No one has claimed responsibility, but Hasina, who was unharmed, has blamed Prime Minister Khalida Zia's administration for the attack. The government has denied involvement.
Meanwhile, senior opposition leader Ivy Rahman, who lost her legs in the grenade attack, died in Dhaka's Combined Military Hospital early on Tuesday, doctors and her family said, raising the toll to 20.
Fearing renewed violence during the two-day strike that started on Tuesday, officials deployed more than 5000 police and paramilitary troops in the capital on Tuesday.
Early election calls
In Dhaka, a city of 10 million people, the streets were empty of most vehicles except rickshaws. Government offices were open, but few employees showed up for work, witnesses said.
"We don't want to see any more death. This repressive government must step down right now," Hasina told reporters late on Monday.
The Awami League has accused Zia's government of corruption, incompetence and harassing political opponents, and has demanded that Zia should step down and call early elections.
The government rejects the allegations and has vowed to remain in power until its five-year term ends in 2006.