The AIADMK supremo, a strident critic of the Rajapaksa administration, said Modi could have avoided the 'ill-advised' move of inviting the head of the island republic, especially with regard to the Centre-state relations.
Jayalalithaa's stiff opposition puts a question mark on her attending the ceremony in Delhi.
A day after MDMK, an ally of BJP, opposed the invitation, DMK said Modi should understand the feelings of the Tamil people on this matter and could have avoided the invite.
She recalled the various resolutions passed in the state Assembly demanding an economic embargo on Sri Lanka among others over the alleged war crimes by the island nation's Army under the Rajapaksa Government against Tamils there during the final stages of "civil war".
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While the UPA Government "chose to ignore" the resolutions by not acting on them, there was a hope that the new regime would be sympathetic to the Sri Lankan Tamil cause, she added.
"It is with a deep sense of anguish that we point this out to the new government to be formed at the Centre.Particularly, with regard to the relationship of the new Central Government with the Government of Tamil Nadu, it would have been better if this ill advised move had been avoided," she added.
Jayalalithaa's slamming of the move came within hours after BJP's state unit disclosed that she has been invited for Modi's swearing-in. The ruling party has not announced if she would participate in the swearing-in.