"For the last time, I am telling the LTTE (Liberation Tigers of Tamil Eelam) to lay down arms and surrender," Rajapakse said.
There was no immediate comment from the Tigers, for whom the loss of Kilinochchi -- the political headquarters of their northern mini-state for the past 10 years -- is a huge blow.
Sri Lankan army chief Sarath Fonseka said taking Kilinochchi was the culmination of a major military offensive that began way back in March 2007 and has witnessed daily fighting for at least nine months.
There were street celebrations in the capital Colombo and elsewhere after news of the town's capture broke.
Military officials said Sri Lankan ground troops had punched through Tiger defences at two locations in the city and quickly taken full control of the area.
The brutal Sri Lankan conflict over the Tigers' demand for a s