Up to 3,000 protesters, including students from religious schools known as madrassas and supporters of the main opposition party, barricaded a highway at Singair in the central district of Manikganj, police said.
"They attacked us with machetes, sticks, bricks and firearms from three sides when we tried to clear the barricade. We fired back in self-defence," Mizanur Rahman, deputy police chief of Manikganj, told sources, adding at least 40 people were injured including policemen.
"The imam of the local mosque used a loudspeaker to rally the protesters. They were shouting slogans for the execution of the bloggers, accusing them of being non-believers and atheists," Rahman said.
Khalilur Rahman, residential medical officer of Singair Hospital, said three young people died of bullet wounds there. A fourth person who was shot died after he was transferred to a Dhaka clinic, police said.
Among the injured, 18 suffered bullet wounds, the medical officer said.
Fifteen people were injured, three by bullets, in another clash between police, ruling party supporters and Islamists in the southeastern resort district of Cox's Bazaar, said private television Maasranga.
The violence broke out as 12 small Islamic parties, backed by the largest Islamic group Jamaat-e-Islami and main opposition Bangladesh Nationalist Party, called a nationwide strike in protest at Friday's police action against Islamists.
Four people were killed, three in police shooting, and about 200 injured during Friday's protests by tens of thousands of Islamists demanding the hanging of bloggers whom they say blasphemed Islam and the Prophet Mohammed.
Tensions have risen over allegedly anti-Islamic blog posts by Ahmed Rajib Haider, who was hacked to death last week near his home in Dhaka.
In recent weeks Haider and fellow bloggers had launched massive protests demanding a ban on the Jamaat-e-Islami, and the execution of its leaders for alleged war crimes in the 1971 independence struggle against Pakistan.
Since Haider's death, Bangladeshi social media has been flooded with his alleged blog posts and with those by other bloggers mocking Islam, triggering protests by a number of Islamic groups and clerics.
The government has warned of tough steps against those who incite social tension, and urged newspapers and blogs not to publish defamatory writings against the Prophet Mohammed.
It has cracked down on anti-Islam blogs and also given police protection to some bloggers in the wake of Haider's murder.
Police have yet to comment on a motive for Haider's killing. But his brother said Haider was targeted by Jamaat's student wing for his online activities.
The killing of Haider was the second attack in Dhaka in less than a month against a blogger critical of Islam and Islamist groups.