Gordon Weiss, a UN spokesman in Colombo, said at least 30 civilians were killed on Monday inside an area the Sri Lankan military had declared as a "safety zone".
Dozens more were killed or wounded over the weekend.
The Tamil fighters, members of the Liberation Tigers of Tamil Eelam (LTTE), say they are committed towards the creation of an independent Tamil state in northern Sri Lanka.
Tony Birtley, Al Jazeera's correspondent in Mullaitivu, said the LTTE appears to have fled the town.
"There are no civilians, just stray cows and members of the Sri Lankan army division which took this town.
"We have been hearing shelling constantly since we arrived here," he said.
"Although the Tamil Tigers seem to be retreating they seem to be putting up some resistance.
"The civilians appear to be retreating with the Tamil Tigers.
"The government is saying they are being forced to - that they are being used as human shields - but we don't know that for certain."
Ban Ki-moon, the UN secretary-general, has expressed concern over the fate of the trapped civilians.
"[Ban] is deeply concerned about the safety and well-being of civilians caught in intensified fighting in the Vanni region of Sri Lanka between the LTTE and the government of Sri Lanka," a statement from his office said.
Ban urged the Sri Lankan government to "accord immediate and absolute priority" towards ensuring the safety of civilians and aid workers, and to ensure that those affected are treated in accordance with international humanitarian law.
The UN's Buhne told Al Jazeera that although the Sri Lankan government had earlier made "very sincere efforts" to minimise civilian casualties, the tactic no longer applied amid escalating tension in the war zone.
"There are just too many soldiers around. You have the [separatists] intermingled with the civilians ... and you have thousands and thousands of well-armed Sri Lankan forces surrounding those civilians," he said.
"We think that it is a tinderbox that we hope will not ignite."
In an interview to Al Jazeera's Birtley, Gotabaya Rajapaksa, the Sri Lankan defence minister, said that government forces exercised extreme caution during the offensive and only fired on Tamil Tiger rebels.
He dismissed the claims of civilian deaths as LTTE propaganda, insisting that no civilians have died in the recent fighting, and that reports to the contrary should not be believed.
|An estimated 230,000 civilians are caught in the crossfire in Sri Lanka's northeast [EPA]
"We don't use indirect fire unless we are 100 per cent certain that those are LTTE camps or bases," Rajapaksa said.
"This is all LTTE propaganda."
Rajiva Wijesinha, of the Sri Lankan government secretariat for co-ordinating the country's peace process, also insisted that the LTTE should be held responsible for civilian casualties.
"For the last three months, the LTTE, have been driving people with them to smaller and smaller areas, and even shooting people who are tying to get out," he told Al Jazeera.
"And as the LTTE get more desperate, they are losing the lives of these people. The government actually declared a safe area a few days back, but then we had information that the LTTE were moving their ammunitions into this area."