The three, including the mastermind of the assault, were nabbed during raids conducted in Panchagarh and Nilphamari districts, Rangpur divisional police chief Humayun Kabir told reporters.
"They all are active members of the outlawed Jamaat'ul Mujahideen Bangladesh (JMB). Mastermind in the recent (priest) murder is among those arrested," he said.
With the detainees, six persons have been arrested in connection with the killing so far, the police official said.
The chief priest of Hindu temple Sri Sri Shantu Santo Gaurio, 50-year-old Jagneshwar Roy, was on Sunday slaughtered in Sonapota village, near the border with India, in a pre-dawn attack by unidentified assailants who also injured two Hindu devotees before fleeing on a motorbike.
The Islamic State had claimed the brutal killing of the priest.
However, Kabir dismissed the claim made by the Islamic State. "JMB operatives committed the murder," he said.
Witnesses said three men, armed with sharp weapons and firearms, had taken part in the killing. The assailants opened fire and hurled bombs while fleeing on a motorbike, they said.
He said that during preliminary interrogation the three arrested had admitted to their involvement in the murder and gave a detailed account of the incident.
Rabindranath Roy, the brother of Jagneshwar, had filed a case over the murder and police lodged another case under the Arms and Explosives Act against three unidentified persons.
