"We want talks with the government to restart," MA Sumanthiran, Tamil National Alliance's senior legislator told reporters in Jaffna.
Direct talks between President Mahinda Rajapaksa's government and the TNA collapsed in January 2012 as Rajapaksa opted to convene an all party meeting instead.
The TNA won a three-fourth strong mandate in the 38 member northern provincial council in yesterday's election - a historic event in the north in the post-LTTE phase.
Sumanthiran said the overwhelming mandate the Tamils have given them was a manifestation of the public will in the north for a political solution to address Tamil issues.
Commenting on the northern election, the US embassy said it remained concerned about reports of election violence.
"Particularly troubling have been reports of involvement by uniformed individuals in these acts".
Meanwhile, President Mahinda Rajapaksa in a statement hailed his government's ability to hold a free election in the north.
In an apparent reference to the TNA, Rajapaksa said certain parties who remained silent when the LTTE ran its campaign of terror were now free to indulge in democratic politics.
