The LTTE is also intensifying the recruitment of child soliders into its ranks as it comes under attack from government forces, Unicef, the UN agency for children, said on Tuesday.
The Tigers, who are fighting for an independent state in Sri Lanka for ethnic Tamils, have always denied forcing children to fight for them.
Government forces say they are on the verge of defeating the LTTE after more than 25 years of civil war.
Estimates on the number of civilians trapped in the conflict zone range from 70,000 to 200,000.
The Tamils Rehabilitation Organisation (TRO) said that the UN had failed civilians trapped by the fighting.
"Given the intensification of the current fighting, any child recruited [allegedly by the LTTE] is likely to be in the line of fire"
James Elder, spokesman for Unicef
The UN was "withdrawing even the remaining few local staff from the conflict zone [and] completely shedding its responsibility of caring for the civilians trapped here," the TRO said on the pro-LTTE TamilNet website.
James Elder, a spokesman for Unicef, admitted that some local staff had requested to leave the war zone amid intense fighting.
"There are two critical things here - one, that women and children be allowed to leave the conflict zone and go to safe areas where they can be reached with support; the other one is that both sides to this fight - the government troops and the LTTE - need to ensure absolute protection for those [trapped] civilians, and that has not been happening," he said.
Unicef has "reliable reports" that children as young as 14 are being forced to fight for the LTTE, Elder said.
"Given the intensification of the current fighting, any child recruited is likely to be in the line of fire," he said.
"These children face the worst kind of horrors - they face being in the front line of an intense conflict during the prime of the childhood. This is clearly against Sri Lankan law and international law."
The UN said in its statement that it welcomed a declaration made last week by the Sri Lankan army of a larger "safe zone" for civilians on the country's northern coastline, but noted that there had been fighting even within that area.
"Reports from yesterday indicate that there was some fighting inside the zone. This fighting led to the deaths and injury to yet more civilians," the UN said.
"The United Nations calls for the Sri Lankan forces and the LTTE to refrain from fighting in areas of civilian concentration."
|Thousands of people have been displaced by fighting between the army and the LTTE [EPA]
But Brigadier Udaya Nanayakkara, a Sri Lankan army spokesman, said there had been no fighting on Sunday in the new no-fire zone.
"There is no resistance from the area, and there are no confrontations there," he said.
Some sick and injured civilians were evacuated from the no-fire zone on Monday by the International Committee of the Red Cross (ICRC).
About 400 injured and their accompanying relatives were shipped out for "further medical treatment," Sarasi Wijeratne, a ICRC spokeswoman, said.
The ICRC earlier said that a "humanitarian catastrophe" was unfolding in the region where "hundreds" of civilians perished this year.
The aid organisation carried out similar sea evacuations twice last week, bringing 745 wounded from Puttumattalan, within the government-declared safe zone, to the government-controlled northeastern seaport of Trincomalee.
More than 70,000 people have been killed over the course of Sri Lanka's civil war.