Police said the group were proceeding in two cars from Thanjavur, 150 km from here, to Rameswaram and planned to take a boat to Katchatheevu to unfurl the tricolour.
They were stopped following a tip-off and arrested.
The group allegedly belonged to 'Hindu Ezhuchi Peravai', a local Hindu outfit at Thanjavur, police said.
Referring to recurrent instances of attacks and arrests of Indian fishermen in the Palk bay, chief minister Jayalalithaa had in her letters to Prime Minister Narendra Modi reiterated her government's opposition to the 1974 and 1976 Indo-Sri Lanka agreements ceding the Katchatheevu islet to the island republic.