RAB arrested six people including the 'mastermind' on Sunday. But Rajshahi Metropolitan Police (RMP) at a press briefing a day later said their investigation did not find any personal motives behind the killing.
Police still suspect militants and Islami Chhatra Shibir had a say in the murder and are looking at their possible motives.
The sociology department teacher was hacked to death near his house in Chouddapai area, adjacent to the campus, on Nov 15.
After the incident, police arrested 11 people and claimed 'Jamaat-e-Islami controlled' militants carried out the murder.
However, RAB arrested six people, including two pro-BNP activists, during overnight raids on Saturday and Sunday in Dhaka and Rajshahi.
At a press briefing on Sunday, the elite police unit claimed Islam was murdered ‘in revenge for his misbehaviour with a female university employee' and there were no connection to the militants.
But Rajshahi Police Commissioner Mohammad Shamsuddin at Monday's media call said, "Further investigation is needed to find the real motive behind Professor Shafiul Islam's murder. But we are closing in on that."
He said they had already arrested Shibir activists 'Sagar', 'Jinnah' and 'Arif' who are among the 11 'involved' in the murder.
"Two of them took part in the attack. The clothes they were wearing at that time have also been recovered. Police found parts of their mobile phones at the murder scene."
However, both Rajshahi metropolitan and RU units of Chhatra Dal at a press briefing Monday rejected the RAB's claim and demanded that the ‘real killers’ be identified.
Earlier, both police and the son of the slain professor, who was known for his devotion to the way of Baul Lalon Shah, had claimed militants were behind the murder.
A self-proclaimed militant organisation 'Ansar al Islam Bangladesh-2' claimed responsibility on a Facebook post hours after the murder.
But RAB said they did not find any militant link.
Claiming they had information that a Jamaat-controlled militant group was involved in the murder, Motihar Police Station OC Alamgir Hossain earlier had said police from Bogra detained four blacksmiths who made the machetes used to kill Prof Shafiul Islam.
The four were brought to Rajshahi on Nov 19, he added.
Hossain had said they also arrested two people who created the 'Ansar al Islam Bangladesh-2' Facebook page and claimed the credit of carrying out the assassination.
They are madrasa teacher Shariful Islam of Bogra and an eighth grader boy.
At Monday's press conference, RMP Deputy Commissioner AKM Nahidul Islam said they were also conducting raids to arrest the chief of the Ansar al Islam Bangladesh-2, who is a Bogra Shibir leader.