In the resolution, the state government sought diplomatic efforts by India to change any possible pro-Lanka stand adopted by the US in a UN rights body.
Chief Minister J Jayalalithaa told the assembly that the US had now reportedly proposed internal probe by Colombo at the United Nations Human Rights Council (UNHRC) and that it was "against natural justice."
The resolution moved by the chief minister said that India itself should move a "strong resolution" at the UNHRC along with the US seeking international probe against those who had committed human rights violations and war crimes in contravention to the international rules and conventions.
Unanimously adopted by the House, the resolution said, "The Tamil Nadu Assembly requests the Government of India that if America takes a stand supportive of Sri Lanka (at the UNHRC), then India must take diplomatic efforts to change that."
Ms Jayalalithaa recalled the earlier resolutions in the Assembly seeking to stop treating Sri Lanka as a 'friendly nation' in the context of the alleged atrocities on ethnic Tamils.
The resolution also said that the AIADMK government would not allow Sri Lankan players and officials to participate in the Indian Premier League sporting fixtures scheduled in Chennai.
Earlier, Opposition parties welcomed the resolution. "This is a timely resolution," DMK's senior leader Durai Murugan said.
The Sri Lankan government has faced accusations from international rights groups that some 40,000 Tamil civilians were killed in the final phase of the military campaign against the Liberation Tigers of Tamil Eelam (LTTE) that ended in May 2009.
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