Shuvendu Adhikari said Hindus, Sikhs, Buddhists, Jains, Parsis and Christians who came to India from Bangladesh were refugees rather than infiltrators.
He made the remarks while referring to the Citizenship Amendment Act at the launch of a digital census process in West Bengal.
Adhikari said central government rules and guidelines applied to people from those communities who took refuge in India by 31 December 2014 after religious persecution or to save their lives.
He said no legal cases should be filed against such refugees and that police should not harass them.
Adhikari separately said people he described as illegal infiltrators should be identified with due caution through legal procedures and returned to their countries of origin.
He also said India had no moral or constitutional duty to support people he classified as illegal infiltrators.