Superintendent of Police (Rural) Koya Praveen said here the group comprised two couples and a 20-year-old youth.
They had been detained last night following an alert issued by Odisha police at a check-post at Nakappalli in the district and were allowed to leave today after due probe.
The scrutiny of documents and verification with the Indian embassy in Iran confirmed that they were tourists and had visited India twice before.
Reaching India in the last week of December, the group visited Delhi, Agra, Uttar Pradesh, Kolkata and reached Bhubaneswar on January 25.
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At a hotel in Bhubaneswar, the staff asked to see their passports. The group left because they didn't like the hotel; but the hotel staff didn't understand this and alerted the police thinking they were fleeing, Pravin said.
Since it was the eve of Republic Day, Odisha police who were on high alert traced their Delhi-registered car to the border with AP, and alerted the police here.
A team of Odisha police too came here today and was satisfied about their credentials, the SP said.