"In the past 24 hours, over 3,000 civilians lie dead on the streets while another 25,000 are critically injured with no medical attention," said the statement.
A senior Sri Lankan media spokesman told the BBC the government did not respond to documents posted on Tamilnet or take them seriously.
Lakshman Hulugalle said the government was waiting for an official "request" from the LTTE.
In contrast, Sri Lanka military officials said earlier that all the civilians who had been trapped in Sri Lanka's northern war zone had escaped.
The government rejected the ceasefire calls, saying that as all trapped civilians had now fled from the area of conflict, there was no reason to stop its offensive.
Charles Haviland, BBC News, Colombo
The Tamil Tiger statement sounds permanent but there is no use of the emotive word "surrender" nor an explicit admission of defeat. A defiant note is sounded when he says that "no force can prevent the attainment of justice for our people".
But the Sri Lankan government, on the crest of a wave of military success, says the fighting has not finished.
The defence minister said the military had yet to clear a small area of jungle where some LTTE members might be hiding, but added that 250,000 people had fled the conflict zone in recent weeks and not a single one had reported seeing the Tamil Tiger leader Velupillai Prabhakaran inside the area.
Army spokesman Brig Udaya Nanayakkara said some 50,000 ethnic Tamils had fled the area over the past three days.
Like all accounts from the war zone, neither claim can be independently verified.
Fighting is still continuing, but there has been no sign of the Tigers' leader, Velupillai Prabhakaran, the Sri Lankan defence minister told the BBC.
For months, tens of thousands of Tamil civilians have been trapped in the war zone, vulnerable to bombardments as the government and Tamil Tiger rebels fought bitterly.
The United Nations says they were being forcibly kept there by the rebels and that more than 6,000 have been killed since January.
The UN has told the BBC the army figures reinforced its view that Sri Lanka's authorities were ill-prepared for the huge influx of internally displaced people.
Refugee camps inland are already badly strained accommodating the huge numbers of those who have fled the conflict.
Both the UN and Western governments have called on Sri Lanka to exercise restraint in its pursuit of a military victory over the Tigers.
1976 Liberation Tigers of Tamil Eelam form in the north-east
1987 India deploys peace-keepers to Tamil areas but they leave in 1990
1993 President Premadasa killed by Tiger bomb
2001 Attack on airport destroys half Sri Lankan Airlines fleet
2002 Government and rebels agree ceasefire
2005 Mahinda Rajapakse becomes president
2006 Heavy fighting resumes
2009 Tigers call for ceasefire after army takes main rebel strongholds, confines Tigers to small coastal enclave
Despite President Rajapaksa's claim of military victory on Saturday, senior officials told the BBC that fighting was still continuing in the area where the LTTE leaders were said to be cornered.
A military spokesman has told the BBC the last remnants of the rebels are trapped in 1.5 square kilometres of jungle. Again, his assertion cannot be verified.
More than 70,000 people have died in the bitter war for a Tamil homeland.
Sri Lanka's army said earlier 70 rebels had been killed trying to escape from a tiny enclave where they are holed up in the island's north-east.
The army says it has cut off rebel access to the sea.
Brig Udaya Nanayakkara said a "process of identification" was going on to identify the 70 rebels killed while trying to cross a lagoon in six boats.
President Rajapaksa is expected to give a nationally televised news conference in parliament on Tuesday, when reports suggest he may officially declare the war over.
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