Hardline Islamic militants in Bangladesh are believed to be behind the murder of a university professor who pushed for a campus-wide ban on full-face veils or burkas worn by students, police said.

Police have arrested at least 20 people questioning over the killing of Shafiul Islam, a sociology professor at Rajshahi University in northwest Bangladesh, Agence France-Presse reported.

Islam was known as a follower of the folk group Baul, whose members adhere to humanism rather than observing a specific religion. Baul is popular in some parts of western Bangladesh.

"We are working on several possible motives behind the killing," Rajshahi police commissioner Mahbubur Rahman said in an interview.

He believed Islamist militants had a hand in the murder.

Rahman declined to specify whether the 20 people arrested in connection with the killing had been affiliated with a religious or political group.

Islam's murder triggered different protests in Dhaka and in Rajshahi, where students boycotted their classes and marched around campuses to protest the killing of the professor on November 16.

An Islamic group called Ansar al Islam Bangladesh-2 claimed responsibility for killing Islam. On a Facebook page, it posted information about its members carrying out the murder.

"Our Mujahideens have today murdered an apostate who had prohibited female students from wearing veils in his department and the classrooms," a posting said. "Beware all the anti-Islamic apostates and atheists!"

The page also mentioned a local news report published in 2010, which stated that the professor asked his female students to remove their veils before coming to his class.

At that time, Islam headed the university's sociology department.

The victim's colleague, Sirajul Islam, another sociology professor, explained that Shafiul banned the burka in his classes to prevent students from using it to cheat.

"He moved to ban full-face veils from the classrooms and examination halls. He thought full-face veils could be used to cheat in the examinations and it was impossible to identify a student who wears a full-face veil," he said.

Bangladesh is the world's third largest Muslim-majority nation, and most of the its population is said to adhere to a moderate form of the religion.