Prime Minister Narendra Modi Saturday urged Sri Lanka to ensure "equality, dignity, justice and self-respect" for its Tamil minority.
Modi made the appeal when a six-member delegation of the Tamil National Alliance (TNA), Sri Lanka's main Tamil political party, called on him.
"The prime minister stressed the need for a political solution that addresses the aspirations of the Tamil community for equality, dignity, justice and self respect within the framework of a united Sri Lanka," an official statement said.
Modi urged "all stakeholders in Sri Lanka to engage constructively, in a spirit of partnership and mutual accommodation, towards finding a political solution".
This should be built "upon the 13th amendment of the Sri Lankan constitution", he said, referring the India-backed amendment of the 1980s which called for devolving autonomous powers to the Tamils.
Modi also assured the TNA delegation of India's continuing support to provide relief, rehabilitation and reconstruction work in Sri Lanka's northeast, the former war zone where thousands have been displaced.
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He said New Delhi's focus would be on projects relating to housing, livelihood generation, capacity building, education, hospitals and infrastructure.
The statement said: "The visit of TNA leaders is part of India's continuing engagement with the government and political parties in Sri Lanka."
The TNA delegation briefed the prime minister on the situation in Sri Lanka and their assessment and expectations regarding devolution and national reconciliation.
The delegation, led by veteran Tamil politician R. Sampanthan, met Indian External Affairs Minister Sushma Swaraj Friday.
The delegation also includes Mavai S. Senathirajah, K. Premachandran, P. Selvarajah, Selvam Adaikkalanathan and M.A. Sumanthiran, all parliamentarians.
Present at the meeting Saturday were Nripendra Misra, principal secretary to the prime minister, National Security Adviser Ajit Doval and Foreign Secretary Sujatha Singh.
The TNA was for years considered the political front of the now vanquished Liberation Tigers of Tamil Eelam (LTTE), which was crushed by the Sri Lankan military in 2009.
After the end of a quarter century of conflict, Sri Lanka battles charges of not engaging with the Tamil community and of killing thousands of innocent Tamils towards the end of the war.