"Terrorism has got to be destroyed," he told parliament delivering a speech to present the government budget for 2009.
The security forces were close to crushing the last remaining resistance of the Tamil Tigers, with the money spent on defence in the last three years having helped to strengthen their capabilities, he said.
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"Now terrorism has been confined to small area in the north," Rajapaksa said. "Soon these areas too will be freed by our security forces."
Rajapaksa said that even at this late stage it was possible for the Tamil Tigers to enter the democratic mainstream, adding that the government was ready to provide the framework for them to do so.
"Let me on this occasion invite the terrorists to lay down warms and enter the democratic society," Rajakapsa said. "If not we will through our military campaign make them go on their knees."
He said the government plans to hold elections in the north once it is cleared of the rebels in the same way it did in the island's east.