President Mahinda Rajapakse said in a televised address to the nation that security forces had wrested control of the town of Pooneryn and the main northwestern coastal A-32 route in the morning.
"The entire A-32 road and Pooneryn was captured by our security forces," the president said.
"On this occasion, I ask (Tiger chief Velupillai) Prabhakaran to lay down arms and immediately come for talks.
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"The best thing he can do for the (Tamil) people in the north is to lay down arms and surrender," he said.
Pooneryn had been a Tiger stronghold since 1993 when the rebels overran the main military base after killing some 700 soldiers in a three-day offensive codenamed "unceasing waves".
The separatist rebels had also used the coastal area to launch artillery strikes against a military airbase on the northern edge of the government-controlled Jaffna peninsula vulnerable to long-range attacks.
Defence officials said the Tigers appeared to have removed their 130-millimeter a