"We put pressure on the group to give up its arms and enter the political mainstream. Terrorists must be wiped out from the Earth," Rajapakse told Japan's Asahi Shimbun ahead of a visit to Tokyo next month.
But he said he was willing to negotiate with the Tamil Tigers if they returned to talks.
"We are ready to negotiate," he said.
The Asahi said it conducted the interview on November 15 in Colombo, before the latest surge in fighting.
At least 18 people were killed Wednesday in two bomb attacks blamed on the Tamil Tigers, including one by a female suicide bomber targetting a government minister from the Tamil minority.
On Tuesday, reclusive Tigers leader Velupillai Prabhakaran vowed to strike back at what he branded the "war of genocide" led by the Colombo government and said peace efforts on the island were a waste of time.
The Tamil Tigers have been fighting for 35 years for a Tamil homeland in the Sinhala-majority island in a conflict that has left tens of thousands of