State Health Minister C Vijayabaskar, accompanied by Health Secretary J Radhakrishnan, met Union Health Minister Nadda and Union Minister of State for the Prime Minister's Office Singh in Delhi.
An official release in Chennai recalled a series of meetings by Tamil Nadu ministers, including Chief Minister K Palaniswami, with Prime Minister Narendra Modi and his colleagues on the issue over the last few days.
"Following these, as a final effort, Vijayabaskar met Nadda and Singh to pressure them for an exemption for Tamil Nadu from the National Entrance Cum Eligibility Test (NEET)," it said.
The minister was accompanied by Mr Radhakrishnan, it added. Tamil Nadu has been seeking an exemption from NEET on the ground that otherwise, it would affect the students of the state.
Meanwhile, DMK working president M K Stalin demanded the resignation of Vijayabaskar for "bungling up" over the NEET issue and "playing with the lives of students".
Alleging that the Mr Palaniswami regime had "failed to protect the interests of the state board students", he asked the chief minister to call on Prime Minister Narendra Modi and "exert pressure" to get the Presidential assent for two Tamil Nadu bills, seeking an exemption for the state from NEET.
In February, the state Assembly had passed two bills, seeking to pave the way for the continuation of the undergraduate medical admissions on the basis of the class 12 marks and exempt Tamil Nadu from the ambit of NEET.
The rival AIADMK (Puratchi Thalaivi Amma) faction, led by former chief minister O Panneerselvam, had also met the prime minister over the issue.
The opposition parties have been upping the ante against the AIADMK regime on the matter, with the DMK staging a human chain protest here last week to press for Presidential assent to the two Bills.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.