Thousands of displaced people are living in temporary camps
The Sri Lankan government has rejected a ceasefire declaration by rebels in the north, saying it was a "joke", and the Tamil Tigers are close to defeat.
The rebels had said their unilateral truce declaration was a response to an "unprecedented humanitarian crisis".
A senior UN humanitarian official, in Sri Lanka, has said an urgent pause in fighting is needed to distribute aid.
The UN says some 50,000 civilians remain trapped in the conflict zone, but the army puts the number at 15,000.
John Holmes, UN Under-Secretary General for Humanitarian Affairs, said the fighting was taking a "terrible toll" on civilians and called on both sides to stop the fighting.
Mr Holmes is on a three-day mission to Sri Lanka.
The rebels said they were following calls from the UN, EU, the governments of India and others in declaring a ceasefire, which they said would come into immediate effect but be maintained only if the government reciprocated.
Spokesman Seevaratnam Puleethevan said it was "purely for humanitarian purposes".
But Sri Lankan Defence Secretary Gotabaya Rajapakse said there was "no meaning" in the declaration.
"They are surrounded, they have no other choice, they are militarily finished," he told the BBC.
"The only thing they have to do - everybody requested, the UN requested, the international community requested - is to release the civilians and lay down their arms and surrender."
The defence ministry reports capturing the village of Valayanmadam, and says 23 rebels surrendered and 200 civilians were "rescued" there on Sunday morning. The report could not be verified independently.
The announcements came as Mr Holmes met Sri Lankan officials to call for access for aid workers to the war zone and government-run camps for thousands of internally displaced persons (IDPs).
From Charles Haviland in Colombo
Outlawed as a terrorist group by many countries, the Tigers are trying to show they are clearly aligned with the UN and Western countries at this point, in contrast to the Sri Lankan government which is continually rejecting the chorus of international calls for a halt in its offensive.
This is not the first time the Tigers have declared their readiness for a ceasefire in recent months. Their past offers have often been sent to key international players with an interest in the Sri Lankan situation.
The government claims the war is nearly at an end and alleges that the Tigers have used past ceasefires to regroup and re-arm.
"We must have access to all IDPs wherever they are, including in the conflict zone," he said.
The rebels have been beaten back to a 12 sq km (5 sq m) area, where thousands of civilians are believed to stuck.
Mr Holmes urged the Tigers to allow those people to leave and said the military should "exercise maximum restraint" and refrain from using heavy weapons.
He said the months of fighting had taken "a terrible toll among the civilian population".
Aid workers have been barred from the area since the fighting escalated last year and the rebels say the government is deliberately blocking food aid - a charge the Sri Lankan authorities deny.
Mr Rajapaksa told the BBC the Tigers were the "the losing side" and denied media reports that he had been stopping food supplies to trapped civilians.
He said that he himself had asked the World Food Programme and the Red Cross to deliver relief to them.
Images from surveillance drones showed there were 15,000 civilians left in the war zone, he added.
A bitter propaganda battle is in progress, the BBC's Charles Haviland reports from the Sri Lankan capital, Colombo.
The Tigers accuse the government of bringing the threat of starvation to civilians inside the war zone.
This undated photo released by pro-Tamil media reportedly shows a government air strike inside a no-fire zone and civilians fleeing
The government and pro-government media accuse the Tigers of keeping Tamil civilians as hostages and murdering people trying to flee their control, including little children.
The Tamil Tigers have fought for an independent homeland for Sri Lanka's Tamil minority since 1983.
More than 70,000 people have been killed in the war, but that figure could now be far higher because of intensified fighting in recent weeks.
Hospitals and government-run camps for displaced people in the north-east have been flooded by people fleeing the shrinking rebel-held zone as the military closes in on the rebels.
A UN document being circulated around diplomatic missions in Sri Lanka estimates that nearly 6,500 civilians have died and 14,000 have been injured since the end of January.
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