The Jaffna peninsula has long been seen as the symbolic heart of a 25-year-old separatist insurgency on the island.
Flight of civilians
Military officials said about 1,700 Tamil civilians had sought shelter with government forces after escaping from the remaining rebel-held areas of the island's north-east.
"In the past two weeks a total of 1,707 civilians have crossed into government-held areas in the north," a military official said, adding that the authorities were arranging emergency relief for them.
Authorities said that they had buried 41 bodies of suspected Tiger rebels killed by security forces in the latest fighting.
The burials came as warplanes bombed and destroyed two LTTE artillery guns, the defence ministry said. It was not clear how many artillery pieces the Tigers still had.
The air force had stepped up raids against the remaining LTTE strong points in the island's north on Tuesday with at least 10 bombing sorties, a ministry spokesman said.
Fighting was also reported around guerrilla-controlled Mullaittivu district.
The LTTE has not commented on the latest fighting, but has admitted losing ground in recent weeks, including in the town of Kilinochchi, which they used as their political base for nearly a decade.