Senior party leader D Raja, who inaugurated the fast in which leaders and party activists took part, said India continued to train Sri Lankan defence personnel despite all parties in the state demanding that it be stopped.
He said the Centre's argument that Sri Lanka was a friendly country and the training was extended under the bilateral agreement was not "valid and not acceptable".
"Bilateral agreements can be reopened and re-negotiated," Raja, National Secretary of the party, said.
Observing that Chief Minister J Jayalalithaa had also written to the Centre demanding that the training be stopped and the personnel be sent back, he said the Centre was not heeding to the demand.
India should strive for a political solution to the Sri Lankan Tamils issue, he added.
The state parties have been strongly opposing any training to Sri Lankan defence personnel on the ground that it hurt the sentiments of Tamil people in view of charges of war crimes against civilians during the last leg of the 'Eelam' war against LTTE in 2009.