At least 71 people were reported to have died in clashes on Wednesday.
The army's move towards Kilinochchi came as Sri Lanak's army chief said that the offensive had cut the fighting strength of the Tamil Tigers to just 3,000 fighters from 12,000.
Lieutenant-General Sarath Fonseka told the Reuters news agency that he expected the group to go underground rather than " fight to the last man" as it continued to come under attack.
"When it comes down to a certain level, they will try to go and mingle with the people or resort to other tactics like they are trying in the east," Fonseka said.
He also said there was no clear timeframe for retaking the territory held by the LTTE because his aim was killing all the fighters rather than seizing ground.
"We don't want to end up in a situation like in Iraq when you're moving fast, but you left behind a whole army who will resort to guerrilla tactics," he said in an interview at army headquarters in the capital Colombo.
"Therefore I don't give a timeframe."
Fonseka said that Velupillai Prabhakaran, the Tamil Tiger founder and leader, had moved from Kilinochchi to somewhere inland from the Mullaittivu port.
More than 70,000 people have been killed since the Tamil Tigers began their fight for an independent homeland in the north and east of the country in 1983.