Tens of thousands of people have been killed since the eruption of the decades-old Tamil separatist insurgency which has grown deadlier since the collapse of a Norwegian-brokered ceasefire in late 2005.
"While my government remains determined to fight terrorism, we are equally committed to seeking a negotiated and sustainable solution to the conflict," Rajapakske told a media conference in the Indian capital New Delhi.
"If those who carry arms against the state are willing to enter a process of genuine negotiation towards a peaceful and democratic solution, the government and the people will reciprocate," said Rajapakse.
"I don't believe in a military solution.
I want a political solution," said Rajapakse, who was on a two-day visit to India due to end late on Saturday.
There was no immediate comment from the Liberation Tamil Tigers of Eelam (LTTE), fighting for a separate state for minority Tamils since 1972.
In seeking peace Colombo was looking for "understanding and assistance