Thirteen were shot dead in the north and northeast and one policeman was killed in clashes with protesters in the western district of Jhenidah, police officials told AFP, adding two people were killed late Saturday.
In the northern district of Bogra at least 10,000 protesters armed with sticks, home-made bombs and other weapons attacked five police stations, forcing police to open fire on them, police Inspector Shamsul Haq said.
"They came from the villages in several groups and attacked our stations in the dawn. Seven people were killed in Bogra district including three who were killed in the worst-affected Shahjahanpur (town)," he told AFP.
Troops have been deployed in Shahjahanpur to strengthen security, he said.
Four people were shot dead in the northwestern town of Godagari after police and border guards opened fire on thousands of protesters from the Jamaat-e-Islami party after they attacked police with sticks and stones, the area police chief said.
The death toll in the clashes over the war crimes verdicts has risen to 72 since the first was announced on January 21, police said, including 56 killed in the four days since Jamaat's vice president was sentenced to death.
Delwar Hossain Sayedee was Thursday found guilty of murder, religious persecution and rape during the 1971 independence war against Pakistan. The sentence triggered violent clashes across the country between rampaging Jamaat supporters and police.
The 73-year-old firebrand preacher was the third person to be convicted by the war crimes tribunal. The verdicts have sparked outrage among Islamists.
Jamaat, the nation's largest Islamic party, says the process is more about settling scores than delivering justice.
The party has called a nationwide strike for Sunday to protest at the verdicts and the killing of its activists by police.
Security was tight in the capital Dhaka with around 10,000 policemen on patrol and shops and schools were closed. Inter-city motorways and roads in the capital Dhaka and the port city of Chittagong were empty.
The United States and United Nations have appealed for calm while global rights group Human Rights Watch has asked the government and Jamaat to act urgently to stem further acts of violence.
On Saturday minority groups appealed to the government for increased security after a series of attacks on Hindu temples and houses by Jamaat supporters, in which one Hindu man was killed. Jamaat denied they were behind the attacks.
An inter-city train was torched, allegedly by protesters, late Saturday.
The war crimes trials of a dozen leaders from Jamaat and the main opposition Bangladesh Nationalist Party have opened old wounds and divided the nation, with the opposition accusing the government of staging a witch-hunt.
The government, which says the war claimed three million lives, rejects the claims and accuses Jamaat leaders of being part of pro-Pakistani militias blamed for much of the carnage during the war.
Independent estimates put the death toll from the war in which Bangladesh won independence from Pakistan at 300,000-500,000.