Chief Minister K Palaniswami said the 12 persons were arrested today in two different instances after they set sail from Jegathapattinam and Kottaipattinam fishing bases in Puthukottai on early hours.
The Chief Minister told Prime Minister Narendra Modi that the arrest came days after External Affairs Minister Sushma Swaraj had met Tamil Nadu ministers and the fishermen representatives separately this month.
"It is unfortunate that these incidents have taken place at a time when our fishermen are hopeful that a pragmatic and permanent solution to this issue would emerge as was discussed at the meeting" with Ms Swaraj, he told PM Modi in a letter.
"This most recent act of the Sri Lankan Navy again creates anxiety and unrest in the minds of our fishermen and vitiates the atmosphere of hope which was generated as a result of these meetings," he said.
It should also be ensured that the livelihood of the poor and innocent fishermen from Tamil Nadu, "who are engaged in their traditional occupation and fish in their traditional waters, are protected," he said.
Mr Palaniswami reiterated that the impounded boats of the fishermen berthed in Sri Lanka should be released immediately.
"I reiterate that the issue of apprehension of our fishermen and release of their boats be taken up at the highest diplomatic level and the Government of India take necessary steps to ensure the safety and security of our fishermen," he said.
Mr Palaniswami sought PM Modi's personal intervention to secure the release of a total of 38 fishermen and 133 fishing boats currently in Sri Lankan custody at the earliest.
He also reminded PM Modi of the state government's demand for a Rs 1,650 crore deep-sea fishing package.