Addressing his supporters at Jantar Mantar, Vaiko, whose MDMK is part of the NDA, said the presence of Rajapaksa would "pollute the sanctity" of Modi's swearing in ceremony.
He also alleged that the Lankan President has committed genocide against the Tamils in the island nation.
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However, Vaiko said that he was not against the NDA Government and greeted Modi, who is set to sworn in as Prime Minister today.
Vaiko was later taken into custody for defying prohibitory orders.
The MDMK chief is opposed to the invitation extended to the Sri Lankan President and had asked the Prime Minister-designate as well as BJP President Rajnath Singh to reconsider the decision.
Vaiko had earlier written a letter to Modi expressing his sadness over the invitation being extended to Rajapaksa for the event.
Recalling that no Sri Lankan Head of State was invited when Atal Bihari Vajpayee was sworn in as Prime Minister, Vaiko had pointed out that even Manmohan Singh had not invited the Sri Lankan President for his swearing in ceremony.
"They did not dare to invite Mahinda Rajapaksa to the swearing in ceremony in 2004 and 2009," he had said.
Tamil Nadu Chief Minister J Jayalalithaa and DMK President M Karunanidhi have also opposed the invite to Rajapaksa.
The Sri Lankan President arrived this morning for the ceremony.