The resolution was moved by Chief Minister J Jayalalithaa and it calls for referendum on separate Eelam among Tamils in Sri Lanka and Lankan Tamils abroad.
Yesterday, the Tamil Nadu government had said it won't allow Indian Premier League (IPL) cricket matches that involve Sri Lankans to be held in the state.
In a letter to Prime Minister Manmohan Singh, Jayalalithaa said the recent agitations in the state regarding a resolution against Sri Lanka at the United Nations Human Rights Council revealed the anguish on the issue.
The strife in Sri Lanka was a lamentable saga launched by the Sri Lankan government - using the Sri Lankan Army against Tamils, the letter said, adding this had resulted in genocide against a defenceless civilian Tamil population and the decimation of thousands of innocent women and children.
These human rights violations had been extensively documented in the international media and condemned globally, it said.