The group demanded that Rajapaksa should not be allowed in India as he had ruled out autonomy for Tamil areas in the island nation.
Rajapaksa arrives on Friday in India for a brief visit that will take him to Bodh Gaya in Bihar and Tirupati in Andhra Pradesh. He returns to Colombo on Saturday.
Termed a "personal visit", the president is avoiding New Delhi despite Sri Lankan concerns over how India will vote in the upcoming UN human rights meet in Geneva.
Last year, India voted for a US-sponsored resolution urging Sri Lanka to go for reconciliation and speedily rehabilitate those derailed by the long running ethnic conflict that ended in May 2009.
The Sri Lankan President has been quoted as saying that he is opposed to granting autonomy to provinces, remarks that are widely seen as going back on promises made earlier to Indian leaders.