The LTTE have denied accusations by the military that civilians inside the war zone are being held as human shields and that they have opened fire on those trying to flee.
The Red Cross on Thursday sent a ferry to the battle zone in an effort to deliver food aid and to evacuate the wounded, but it could not reach the coastline due to the continuing violence.
"The situation is becoming desperate because of the fighting, which is intense and uninterrupted," Sarasi Wijeratne, spokeswoman for the International Committee of the Red Cross (ICRC) said.
The developments come a day after the US president called on both sides of Sri Lanka's conflict to stop the fighting to protect civilians.
Barack Obama's demand that the Sri Lanka government end "indiscriminate shelling" and the Tamil Tigers stop using civilians as shields came as the UN Security Council expressed "grave concern" over what it described as a "worsening humanitarian crisis".
Speaking to reporters at the White House on Wednesday, Obama warned that the situation in the South Asian country could turn from a humanitarian crisis to a full-blown catastrophe.
He urged the Tamil Tigers to stop fighting and release civilians as a first step towards peace.
"Their forced recruitment of civilians and their use of civilians as human shields is deplorable. These tactics will only serve to alienate all those who carry them out," he said.
He also said the government should stop the use of heavy weapons in the conflict zone and give the UN and Red Cross staff access to the 190,000 displaced civilians.
"Now's the time, I believe, to put aside some of the political issues that are involved and to put the lives of the men and women and children who are innocently caught in the crossfire, to put them first," Obama said.
"More civilian casualties and inadequate care for those caught in resettlement camps will only make it more difficult to achieve the peace that the people of Sri Lanka deserve."
UN calls for action
After the Security Council's first meeting on the crisis on Wednesday, Vitaly Churkin, the Russian ambassador to the UN, read a statement saying its 15 members called for "urgent action" by all parties to ensure the safety of civilians.
The press statement condemned the LTTE for its acts of "terrorism" and alleged use of civilians as human shields, demanding that it lay down its arms, while saying that Sri Lanka's government reserved the right to "combat terrorism".
|Satellite images indicate heavy weapons are being used in civilian areas
But it also said the government must "fulfil its commitment" over the use of heavy calibre weapons in areas with high concentrations of civilians.
Al Jazeera's John Terrett, reporting from the UN headquarters in New York, said that while Western diplomats were publicly hopeful that the UN may do more to ease the crisis, some countries, such as Russia, China, Libya and Vietnam remained opposed to more action over what they consider an internal matter.
Wednesday marked the first time that the council had held formal briefings on the crisis in Sri Lanka, although informal consultations had been held before.
The council's press statement is not legally binding but Kyung-Wha Kang, the UN's deputy high commissioner for human rights, told Al Jazeera that any condemnation would resonate with those involved in the crisis, although he conceded that resolutions or presidential statements were thought to carry more weight.
"We believe it has influence. It clearly keeps up the profile as an international issue on the agenda and I think it does register with the players on the ground," he said.
Wednesday's statements by the UN and Obama came hours after rights group Amnesty International demanded urgent action by the council and an investigation into "the mounting evidence of serious violations of international law".
Tens of thousands of people have fled the fighting in recent weeks to state-run refugee camps, but the UN estimates that about 50,000 civilians remain trapped in the narrow strip of land still held by the Tamil Tigers.
Hundreds are thought to have been killed in recent days in heavy shelling.