Rajapakse told the Tamil National Alliance (TNA) party, formerly a front for the defeated Tamil Tiger rebels, that he was working to achieve a political resolution, his office said.
"Trust me, and together we can find a solution to the problems faced by all our people," the president said.
"But I will not bow down to terrorism, and what the terrorists wanted I will never give," he added, referring to the demand for an independent homeland.
The Tamil Tiger rebels were crushed by security forces in May last year after 37 years of fighting.
The United Nations has said up to 100,000 people were killed in the conflict.
Since the defeat of the Tigers, the TNA has taken a moderate line and has had several meetings with Rajapakse, including a high-profile discussion last September on the subject of peace and reconciliation.
However, the TNA contested April parliamentary elections on a platform of launching a civil disobedience campaign to press long-standing demands for regional autonomy