MDMK chief Vaiko had separate meetings with Modi and BJP President Rajnath Singh in this regard in Delhi.
"Rajapksa is the butcher of Tamils. Mr Modi should reconsider the decision to invite him (for the swearing-in ceremony on May 26)," Vaiko told reporters after meeting the Prime Minister-designate.
Asked what was Modi's response, Vaiko did not say anything.
Ealier in the day, he met Rajnath Singh and demanded that the party should "avoid" the presence of Rajapaksa at Modi's swearing-in ceremony.
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PMK also urged Modi to reconsider his invitation to Rajapaksa.
"Respecting the feelings of the people of Tamil Nadu, the invitation to Rajapaksa for the swearing-in of Narendra Modi-led NDA should be reconsidered," party founder S Ramadoss said in a statement in Chennai.
DMK president M Karunanidhi said the invitation was "not acceptable and unwelcome" by Tamils all over the world and urged him to drop the initiative.
"The Centre should deeply ponder over whether a person who had killed lakhs of Tamils, indulged in ethnic cleansing and someone who had waged a war against his own people should participate in the swearing-in of Narendra Modi and request them to drop the initiative," he said in a statement in Chennai.
Arch rivals AIADMK and DMK closed ranks yesterday to stoutly oppose the invitation extended by Modi to Rajapaksa for his May 26 swearing-in with Chief Minister J Jayalalithaa saying it is "unfortunate" and tantamounts to "rubbing salt into the wounds of the already deeply injured Tamil psyche.