"There's no fighting taking place. After capturing the frontline there is a large influx of civilians being rescued," he said.
"There's no shooting taking place in that area."
After the government's deadline for the LTTE to surrender expired, Seevaratnam Puleedevan, secretary-general of the group's peace secretariat, said the Tigers would never lay down their arms.
"LTTE will never surrender and we will fight and we have the confidence that we will win with the help of the Tamil people," the Reuters news agency quoted him as saying.
Since late 2007, the government has made clear it aims to "wipe out" the LTTE, which has been fighting for decades for a Tamil homeland in Sri Lanka's north, arguing that ethnic Tamils are marginalised under the Sinhalese majority government.
Government forces mounted their "final assault" after the deadline ran out at noon (06:30 GMT) on Tuesday.
The military said it had reached the shoreline, suggesting it had cut the LTTE-held territory in half.
As part of the operation, soldiers took control of the only medical facility in the 17sq km "no-fire zone" - a makeshift hospital run by the International Committee of the Red Cross (ICRC) in Puttumatalan, Sarath Fonseka, a Sri Lankan army chief, said.
An emailed statement from the LTTE said that about 1,000 civilians had been killed in the assault.
The ICRC warned the situation was "nothing short of catastrophic" and said that hundreds of civilians had been killed in the past 48 hours, but did not blame either side.
The LTTE called on the UN and the world community to help civilians in the area, which they said was now a "bloodbath".
International organisations are increasingly concerned for the welfare of civilians, with tens of thousands of people having to escape the fighting and take refuge in government shelters.
More than 49,000 people have poured out of the region since the government deadline ran out.
Sarah Crowe, a Unicef spokesperson, told Al Jazeera: "Things are on a knife edge at the moment. It is a human avalanche.
"Some 65,000 people are crammed into overcrowded camps. What we're concerned about now is, with this new flood of people coming in, the camps will be so overcrowded that they will be unable to cope.
"We know that water and sanitation are dire and that children are already quite malnourished."
Human Rights Watch (HRW) said on Tuesday that between 50,000 and 100,000 people remain stranded in the "no-fire zone".
Brad Adams, HRW's Asia director, said: "Both sides need to show far greater concern for civilians, or many more civilians will die."
However, Lakshiman Hulugalle, a defence ministry spokesman, said that the government could cater for the refugees.
"We have been looking after more than 70,000 refugees for the last couple of months,' he said.
"Their welfare is being looked after. Once their registration is done, their basic needs are being looked into."
The UN has repeatedly accused the military of shelling the "no-fire" zone, and the LTTE of preventing civilians from leaving, in effect using them as human shields.
Both sides reject the claims.
The UN says at least 4,500 civilians have been killed in the past three months of heavy fighting and another 12,000 injured.
The military's final operation to crush the LTTE set off protests by expatriate Tamils in London and Paris, the latest in weeks of demonstrations against the offensive in cities across the world.
In Paris, around 180 people were arrested and four injured after protesters blocked an intersection and threw objects at buses and police, French authorities said.