The UN believes that dozens of people are dying there every day.
However, the government said that more than 23,000 people fled the region last month and between 30,000 and 40,000 civilians remained there.
The military said that it had taken the village of Puthukkudiviruppu in the northwest, the last territory held by the LTTE apart from the "no fire" zone, where they recovered 250 LTTE bodies.
The LTTE has not made any comment on the government claims which cannot be independently verified because journalists are prevented from entering the conflict area.
The "no fire" zone was established by the government to provide a place of refuge to civilians caught up in fighting.
Sophie Romanens, from the International Committee of the Red Cross, told Al Jazeera that civilians had fled to the "no fire" costal area to escape fighting and to find food and medicine over the past few weeks.
"Our concern now is that the area has been regularly affected by fighting. And now ... we have growing concern for their [the civilians] safety and wellbeing," Romanens said.
"It is an area which is now full of people - one shelter next to the other. And the fighting is very close."
"These people are completely dependent on aid from the outside."
The Tamil Tigers have been fighting for an independent Tamil homeland in the north of the island nation for more than 25 years.
More than 70,000 people have died in the civil war.