Many civilians have been forced to flee the fighting
The UN, backed by the US and Britain, has urged the Sri Lankan government and Tamil Tiger rebels to back a "humanitarian pause" in fighting.
A senior UN official said the civilian population trapped in the conflict zone in the north was not being allowed out.
Amnesty International said on Friday that thousands of civilians were increasingly at risk in the conflict.
Troops have pushed the rebels from most of the territory they held during heavy fighting in the past few weeks.
The rebels are now restricted to a small area of jungle and coast in Mullaitivu district.
Rights and aid groups have continued to criticise both the government and Tamil Tiger rebels over civilian casualties.
United Nations humanitarian chief John Holmes told reporters that the main concern was that the Tigers were not allowing trapped civilians to leave the area. The UN was pressing the authorities for access to the combat area, he said.
Thousands of civilians have been displaced by the fighting
"We suggested the idea of some kind of humanitarian pause to allow that to happen and to allow the civilian population to leave," news agency AFP quoted Mr Holmes as saying.
"This is an extremely worrying situation and therefore, our first appeal is to the Tamil Tigers to let the civilians out in a safe and orderly fashion."
Senior US official Rosemary DiCarlo also voiced her government's "concern at the deteriorating situation in Sri Lanka".
"We certainly condemn the fact that the [Tamil Tigers] use civilians as human shields... We call on them to lay down their arms, renounce violence and negotiate with the government," Associated Press quoted Ms DiCarlo as saying.
She also criticised government troops for continuing to shell areas heavily populated by civilians.
"We are very concerned that the government of Sri Lanka continues its shelling of areas where there are large numbers of civilians, very close to hospitals, very close to civilian facilities," she said.
"The death toll of the civilians continues to rise, and that's a real concern.
"We've had promises, but we need to see results. The government of Sri Lanka must pay more attention to protecting the civilians in this conflict," she said.
Amnesty International said that tens of thousands of people trapped in government-designated "safe zones" in the north-east were becoming more exposed because of the escalation in fighting.
Amnesty also called for an immediate truce to allow aid to reach trapped civilians and ensure safe passage for all those who wished to leave.
It called on the UN and international donors to put pressure on Sri Lanka to ensure unimpeded humanitarian access to camps for displaced people.
"The deliberate firing on civilians by either side constitutes a war crime," said Sam Zarifi, director of the Asia Pacific region at Amnesty International.
"We cannot stress enough the importance of an immediate pause to allow the displaced to leave before thousands more are killed."
The Tigers have been fighting for a separate homeland for the minority Tamil community for more than 25 years now.
More than 70,000 people have been killed in the civil war.