In the first arrests police have made outside the cafe, Gias Uddin Ahsan of the private North South University was detained late Saturday along with two other people and is expected to appear in a court in the capital to face charges Sunday.
20 foreigners killed in Dhaka cafe siege
Police allege that in May he rented a flat he owns -- without registering the tenants' information as required by law -- to some of the gunmen responsible for the attack claimed by the Islamic State group.
The professor was arrested for "renting the house to the Gulshan (cafe) attackers and hiding information," police said in a statement, adding that the men had "gathered at the flat" prior to the attack.
Bangladesh authorities made submitting tenants' information to the nearest police station mandatory in recent years as part of efforts to curb crime and extremist activities.
The other two people who were arrested included a nephew of the professor and the manager of the apartment building, police said.
Police seized sand-filled cartons from the flat, which they suspect were used for storing grenades, the statement added.
At the time of the cafe seige police said they had detained two people including a teenage kitchen assistant, who died in custody, with his family alleging torture.
This Muslim victim refused to abandon his friends during Dhaka carnage
Rights groups have also expressed concern for two attack survivors they say are being held by investigators, though police deny the two are in their custody.
NSU, Bangladesh's leading private university which caters to children of the country's elite, has come under scrutiny before after its students were linked to extremist activities.
One student was detained in the United States in 2012 and later got a lengthy prison sentence over an alleged plot to blow up the New York Federal Reserve bank.
In December seven NSU students were convicted and sentenced for the 2013 murder of an atheist blogger, the first in a spate of such killings of secular activists and religious minorities.
Hostage-takers were from Bangladesh group, not Islamic State: minister
Last week one of the university's former students was shot dead by police on the day of Eid festival after he and several other Islamist extremists attacked the country's largest prayer congregation with guns and explosives killing three.
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