"I want to tell the Tigers 'lay down arms and surrender to security forces'," the president told a public rally in the northwestern district of Kurunegala.
He said the Liberation Tigers of Tamil Eelam (LTTE) had been encircled in a narrow strip of land and had taken thousands of civilians hostage.
"They must let the civilians go and then unconditionally give themselves up," he said echoing a call by Sri Lanka's US-led aid donors who have asked the Tigers to negotiate terms of surrender.
The president, who earlier in the week vowed to defeat the guerrillas within days, said the Tiger guerrillas had no choice but to surrender.
"I must warn them we will not halt our operations against terrorism until we reach our final objective," he said to resounding applause from thousands of supporters.
The military said the Tigers had been restricted to an area less than 100 square kilometres (38 square miles) in the northeastern district of Mullaittivu where officials estimate 120,000