The UN has been criticised for failing to stop escalating violence
A senior UN official has urged Sri Lanka's Tamil Tiger rebels to lay down their arms and let the UN help trapped civilians to leave the conflict zone.
Claude Heller, Mexico's ambassador at the UN in New York, spoke to reporters after chairing an informal meeting of the UN Security Council on the issue.
While the 15-strong Council passed no resolution on the conflict, Mr Heller said he was voicing members' concerns.
Sri Lanka's army says it has closed in on the last area of Tiger resistance.
It says that more than 100,000 civilians have escaped from the rebel-held area in the north-east but many remain trapped.
Sri Lanka's President, Mahinda Rajapaksa, has ruled out a pardon for Tiger leader Velupillai Prabhakaran if he is captured alive by advancing government soldiers.
On Wednesday, Sri Lanka's government said the rebels' media co-ordinator, Daya Master, had given himself up, along with an interpreter involved in talks with the press and foreign diplomats.
Correspondents say the surrenders will be a major setback for the rebel leadership if they are confirmed.
Tamil Tiger leaders have insisted rebels should commit suicide by swallowing cyanide capsules rather than be captured.
Wednesday night's meeting of the Security Council was an informal session in the UN basement, called by France in response to the suffering of the people trapped in the conflict zone.
The Council has been criticised by advocacy groups for failing to act in the face of the escalating violence but two of its permanent, veto-wielding members, Russia and China, insist the war is an internal conflict that does not threaten international peace and security.
Mr Heller said there was deep concern about the plight of the civilians and he accused the Tigers of using people as human shields in the conflict zone.
"We strongly condemn the LTTE [Liberation Tigers of Tamil Eelam] terrorist organization for the use of civilians as human shields and for not allowing them to leave the area of conflict," he said.
"In this regard, the Security Council members... demand that the LTTE immediately lay down arms, renounce terrorism, allow a UN-assisted evacuation of the remaining civilians in the conflict and join the political process for dialogue in order to put an end to the conflict."
Mr Heller also called on the Sri Lankan government to allow aid agencies in to help those affected by the fighting.
Because the UN meeting was informal nothing binding which has to be followed up with action was agreed, the BBC's Laura Tevelyan reports.
But Western diplomats say a strong statement of concern has been sent from New York which will be closely followed by both the Tamil Tigers and Sri Lanka's government.
France and Britain are talking separately about whether it may be possible to send boats to rescue people who remain trapped on beaches in north-eastern Sri Lanka.
The US state department has released satellite images of civilian camps consisting of 25,000 tents in a government-designated safe zone - which the army says will not be attacked by heavy armaments - in the dwindling amount of territory still held by the rebels.
TAMIL TIGER DEFENCES BREACHED BY SRI LANKA ARMY
12km-long defensive earthworks constructed by Tamil Tigers using mechanical diggers
Sri Lankan army uses explosives to destroy a 3km section
Gap allows thousands of refugees to flee Tiger-held territory
The state department says 120,000 people remain in the war zone.
Sri Lanka's government says that about 30 civilians have been killed in recent days, including 17 in a rebel suicide attack.
While those figures cannot be independently verified, the UN estimates that more than 4,500 civilians have been killed in the past three months.
Sri Lanka's army says it is poised to attack the Tamil Tiger leader and estimates that only 300-400 Tamil Tiger fighters remain, confined to an area no bigger than 12 sq km (five square miles).