"We cannot import a solution and it cannot be a Rajapaksa-Sampanthan (main Tamil party leader) agreement," Rajapaksa was quoted as telling Prasad.
He also underlined that all Sri Lankan political parties must join hands to find an all-inclusive settlement to the ethnic issue.
Prasad, Deputy Leader of Opposition in the Rajya Sabha, is leading a five-member delegation on a five-day visit to Sri Lanka.
Besides Prasad, the delegation includes Shiv Sena leader Suresh Prabhu, senior journalist Swapan Dasgupta, retired IFS officer Vivek Katju, RSS representative Ram Madhav and human rights activist Monika Arora.
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During the team's Jaffna visit, the Sri Lankan Navy had announced the arrest of some 49 Indian fishermen inside Sri Lankan waters.
Rajapaksa's office said the delegation had raised the issue of the fishermen's arrest and Sri Lanka's efforts to find a political solution for devolving powers to the Tamil-dominated northern province.
The President assured Prasad that the northern provincial election would be held in September.
The delegation's visit has been organised by the India Foundation in New Delhi and Colombo's Bandaranaike Centre for International Relations.
Sri Lanka's cabinet yesterday deferred its plan to introduce a controversial new bill aimed at diluting powers of provincial councils including in the Tamil-dominated north, a move that has raised concerns in India.
There has been a flurry of government action in recent days on the 13A which would culminate with the bill being presented in parliament later this month at the behest of Rajapaksa's nationalist allies.