"If the government of India does not come forward to halt the war in Sri Lanka within two weeks, then the MPs from Tamil Nadu would be constrained to give up their posts," the deputies said in a statement issued late Tuesday.
It urged the government to take "immediate steps to stop the war ravaging the island nation for three decades and claiming several thousand lives including innocent children".
Sri Lanka's ethnic Sinhalese-dominated government is engaged in one of its biggest offensives against the Tamil Tigers, who control part of the north of the island and want to carve out a separate state.
The Sri Lankan government says it has killed around 7,500 Tamil Tigers since January, when it pulled out of a Norwegian-backed truce.
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The United Nations says 230,000 people have been displaced in the recent wave of fighting.