Kumaratunga's trump card has been to offer the Tamils regional autonomy in the north and east.
The mainly Sinhala province also has a large population of Indian-origin Tamils working in plantations.
Analysts say the plight of Sri Lankan Tamils has an emotional and often a political echo in Tamil Nadu.
Patching up foreign ties and reconciliation with the aggrieved Tamils are the most important tasks facing Sri Lanka's rulers.
But many Sri Lankan Tamils abroad are not convinced by the government's assurances.
Warm relations with India, too, rest in part on reconciliation with the Tamils.
All this is paid for with contributions, mostly from expatriate Tamils, and profits from businesses, such as restaurants and shipping.
The DMK is the main opposition party in the southern state of Tamil Nadu, which has a large population of Tamils.
Of its 17 members, 11 wanted a far-reaching system of devolution that would have satisfied most moderate Tamils and isolated the Tigers.
They were never fully accepted there, they say, being seen as quasi-Tamils.
Still, despite the LTTE's past efforts to kill off moderate Tamils, the Tamil community is not lacking in political parties or leaders.
What also sets the Tamils apart from northern communities and, indeed, from other Dravidian groups, is a strong sense of belonging to their homeland.
The issue of Sri Lankan Tamils was also raised in parliament by MPs from the DMK and AIADMK, another regional party from Tamil Nadu.
However, it is the second count that is Mr Rajapaksa's greatest challenge: reaching a political settlement with Sri Lanka's marginalised, intimidated and livid Tamils.
So, for the purposes of local politics, Tamils, Gujeratis, Keralans and Bibaris were redefined as a single tribe, and began to behave as such.
In a letter to Prime Minister Manmohan Singh, Ms Jayalalitha said people in Tamil Nadu had been angered by "barbaric acts" against Sri Lankan Tamils.
She jostles for space among the throngs of internally displaced Tamils peddling their rations near the hospital in Vavuniya in the north of Sri Lanka.
Though Tamils are not excluded from the tours, few attend.
ECONOMIST: A rebel stronghold becomes an unlikely tourist trap
But Sri Lankan Tamils should also rejoice.
ECONOMIST: Sri Lanka after the war: Victory's rotten fruits | The
After securing 194 of the 238 local councils contested in the polls, Chandrika Kumaratunga, Sri Lanka's president, described the results as a renewed mandate for her to push ahead with proposals to grant limited autonomy to Tamils living in the war-afflicted north and east of the island.
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