Sri Lankan television footage of civilians receiving food aid. Aerial footage provided by Sri Lanka air force.
Sri Lanka's army says it is in the "final stage" of operations against the Tamil Tigers with troops just 1.8km short of "dominating the whole coast".
The government has rejected international calls for a truce, saying all trapped civilians would be "rescued from rebel control" within two days.
The rebels' website says the entire area under their control is "in smoke".
The United Nations is sending a new envoy to discuss the crisis, but says a bloodbath "seems to be inevitable".
The Sri Lankan military says troops moving along the coast in a pincer movement have just 1.8km (1.1 miles) of shoreline to capture, the BBC's Sri Lanka correspondent Charles Haviland reports from Colombo.
Sri Lankan government spokesman Anusha Palpita was quoted as saying by the AFP news agency on Friday: "The president assured that within the next 48 hours the thousands of Tamil civilians will be freed from the clutches of the Tamil Tigers. All territory will be freed from Tiger control."
None of the reports, claims and counter-claims from the fighting zone can be independently verified.
UN spokesman Gordon Weiss told the BBC that the next 24 to 48 hours would be critical.
"We have been warning about a bloodbath for many months and as the battle has reached this culmination it has become a truly terrible situation for civilians caught inside," he said.
Mr Weiss said the Sri Lankan military has consistently said it will complete what it believes is the final phase of the war and that there did not appear to be "any end except the end game".
He also said the UN had lost contact with the two doctors who had been providing information on casualties in the conflict zone.
The UN says it is sending the secretary general's chief of staff, Vijay Nambiar, to press for an end to the fighting.
Mr Nambiar is returning to Sri Lanka a month after he met President Rajapaksa but failed to secure access to the war zone for humanitarian teams.
Mr Weiss told the BBC it was not clear whether Mr Nambiar would arrive in time to negotiate the prevention of many more deaths.
The authorities and the rebels blame each other for civilian deaths.
The International Committee of the Red Cross (ICRC) has called the crisis an "unimaginable catastrophe".
British International Development Secretary Douglas Alexander said it was "deplorable" that the ICRC is unable to evacuate war wounded to safety or provide aid to the 50,000 civilians trapped in the conflict zone.
Mr Alexander said that there was "no justification for allowing such needless suffering" and both the government and the Tamil Tigers must guarantee safe access to the ICRC.
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