Responding to her remarks, state Health Minister C Vijayabaskar said an ordinance in this regard would be submitted to the Centre tomorrow morning.
The development comes after Tamil Nadu Chief Minister K Palaniswami, state ministers and Lok Sabha Deputy Speaker M Thambidurai had multiple meetings with Prime Minister Narendra Modi and other central ministers over NEET.
Tamil Nadu, which had initially sought permanent exemption from NEET by passing two Bills in the Assembly, later made efforts to be out of its ambit for at least a year or two.
However, efforts were on to prepare students for common tests in future, he said.
Sitharaman said although students who had qualified in NEET included those from the state board, students from rural Tamil Nadu were largely out of it.
"The Centre is ready to cooperate in case the Tamil Nadu government comes up with an ordinance seeking exemption from NEET for government colleges," she said adding the exemption was only for a year.
Barring government colleges, NEET has already been implemented for other institutes, the Union minister said.
Terming Sitharaman's remarks a "good news" Vijayabaskar said, "I thank Union Minister Nirmala Sitharaman and Prime Minister Narendra Modi on behalf of Tamil Nadu government and students."
Tomorrow morning the state ordinance seeking exemption from NEET would be submitted to the Centre. A government secretary would be leaving for Delhi tonight and the ordinance would be promulgated after consultations with the chief minister, he said.
The state health minister said the Tamil Nadu government was confident of the Centre's nod for the ordinance and under no circumstances had the Centre been "negative" about the proposal.
Vijayabaskar said care was being taken to ensure that the proposed move does not face any legal hurdles and the government was confident of completing the admission process ahead of the month-end deadline.
In future, students would be well-prepared for NEET and the syllabus too would be oriented likewise, he said.
Leader of Opposition in Tamil Nadu Assembly M K Stalin hit out at the centre and state governments accusing them of "staging drama" on the issue and "betraying" students.
Actor Kamal Haasan, meanwhile, in a tweet, asked the state government to "talk immediately" (with the Centre) on the NEET issue since the matter involved the future of students.
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