"I call on the private sector, both local and foreign, to invest in the north and east."
The speech came a day after the government said all top Tamil Tiger leaders had been killed in a final battle with army commandos in the north-east.
Rajapakse also said he appeals to Sri Lankans, especially professionals, who migrated because of the ethnic conflict, to return to the island.
"I appeal to our professionals - our engineers, doctors, accountants and other professionals - to come back to their motherland and take part in its development.
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Rajapakse also said the government will move fast to find a lasting political solution to the ethnic problem but said there was no need for foreign intervention in such a settlement.