Modi told a delegation of the Tamil National Alliance (TNA), Sri Lanka's main Tamil political party, that Colombo must address the "aspirations of the Tamil community".
This, he said, needed to be done by building on the India-backed 13th amendment to the Sri Lankan constitution that seeks to devolve autonomy to provinces - by extention the Tamils who dominate the island's northeast. The TNA has accused the Sri Lankan government of attempting to dilute the provisions of the 13th amendment and of trying to change the demography of the northern and eastern provinces, the former war zone.
"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 here said after the Modi-TNA meeting.
Modi urged "all stakeholders in Sri Lanka to engage constructively, in a spirit of partnership and mutual accommodation, towards finding a political solution".
The prime minister also assured the TNA delegation of his government's support to provide relief, rehabilitation and reconstruction in the north and east of Sri Lanka where tens of thousands were displaced by war.
He said New Delhi would focus on projects relating to housing, livelihood generation, capacity building, education, hospitals and infrastructure.
The statement underlined that the visit of TNA leaders "is part of India's continuing engagement with the government and political parties in Sri Lanka".
It was the clearest indication after Modi became prime minister in May that the BJP-led government would not depart from the policy of the earlier Congress-led government vis-a-vis Sri Lanka.
Delegation leader R. Sampanthan said after arriving in India that Tamils in Sri Lanka had their roots in India.
"Their culture is India and everything is Indian. So I think India is one country that can play a major role (in Sri Lanka)."
The TNA delegation briefed Modi on the situation in Sri Lanka and their assessment and expectations regarding devolution as well as national reconciliation following the end of the military conflict.
The delegation met External Affairs Minister Sushma Swaraj and former prime minister Manmohan Singh Friday.
The delegation also includes Mavai S. Senathirajah, K. Premachandran, P. Selvarajah, Selvam Adaikkalanathan and M.A. Sumanthiran, all MPs.
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 leaders and of killing tens of thousands of innocent Tamils towards the end of the war.
India deployed troops in Sri Lanka's northeast in 1987 in a bid to end Tamil separatism. The troops ended up fighting the LTTE and returned home in March 1990 after losing nearly 1,200 men.