The arrest of Rehman, 37, followed a joint operation by Odisha and Delhi Police, Police Commissioner R.P. Sharma told the media.
Rehman was suspected to be a member of the Al Qaeda in Indian Subcontinent (AQIS) and had links with contacts in other countries such as Pakistan and Britain, he said.
The arrest took place at his house in Paschima Kachha village on Tuesday night.
Sharma said Delhi Police had come to know about Rehman's links with the AQIS after tracking his telephone call records.
A PhD on Islam from Deoband in Uttar Pradesh, Rehman ran a seminary in Cuttack district. Most of his students hail from Jharkhand.
According to Delhi Police, Rehman was engaged in recruiting members for Al Qaeda.
However, there was no indication that he was involved in or planning any terrorist activities in Odisha, Sharma said.
Sharma said the suspect's elder brother, Tahir Ali, was earlier arrested in 2001 terror attack on the American consulate in Kolkata.
Rehman would be produced in a Cuttack court and then taken to Delhi for further investigation.
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