The Times says that the deaths happened during the Tigers' last stand
The Sri Lankan government has strongly denied allegations that more than 20,000 civilians were killed during its recent onslaught against Tamil rebels.
The figures published in The Times newspaper in the UK - quoting official documents and witness accounts - is far higher than previously thought.
A senior official from Sri Lanka's Centre for National Security told the BBC the accusations were totally false.
The UN says that there are no confirmed estimates of civilian casualties.
The last time it gave an estimate was about two weeks before the end of the war, when it said that 6,500 people had died.
But the UN Resident Co-ordinator for Sri Lanka, Neil Buhne, has told the BBC that he has no final figure in part because access to displaced people in camps is restricted by the government.
The government's denials are likely to be dismissed by many of its critics, who accuse it of repeatedly giving out inaccurate information about what has been happening in the north.
Aid agencies point out that its insistence that only about 110,000 civilians were trapped in fighting in the north - and its condemnation of UN figures saying the true figure was twice that - was followed by more than 250,000 civilians emerging from the area.
The Times on Friday published photographs showing a devastated area in the former conflict zone where an estimated 100,000 people were sheltering.
The government says that it is doing all it can to protect displaced people
It said that more than 20,000 Tamil civilians had been killed in the final throes of the war, most as a result of government shelling.
Video evidence published by The Times suggests that the Tamil Tigers established mortar positions and military encampments within camps for displaced people, which were then shelled by the military.
Government forces were meant to have stopped using heavy weapons on 27 April.
From that time onwards they were supposed to observe a no-fire zone where 100,000 Tamil men, women and children were sheltering.
The paper says that it compiled its evidence using aerial photographs, official documents, witness accounts and expert testimony.
"The offensive ended Sri Lanka's 26-year civil war with the Tamil Tigers, but innocent civilians paid the price," the Times says.
It says that the evidence was compiled from confidential UN documents which record 6,500 civilian deaths in the no-fire zone up to the end of April, with an average of 1,000 civilians killed each day until 19 May, the day after Velupillai Prabhakaran, the leader of the Tamil Tigers, was killed.
'Jilted old woman'
A senior official from Sri Lanka's Centre for National Security, Laksham Hullegalle said there had been no shelling or killing in the zone, and that the photographs were "totally unbelievable".
Fighting intensified in the latter stages of the war
"The decision was taken by the government not to use any heavy weapons from the beginning of this month," he said.
"From that time onwards there was no heavy shelling."
Mr Hullegalle said there was a possibility the photos were fake and that there had been no corroborating evidence from civilians who fled the area and no bodies discovered.
The permanent secretary to the Sri Lankan Ministry of Foreign Affairs, Dr Palitha Kohona, also dismissed the report.
"I am bemused that The Times, like a jilted old woman, is continuing a bitter campaign against Sri Lanka based on unverified figures and unsubstantiated assertions," he said.
"The simple fact is that Sri Lanka eliminated a detestable terrorist group and in the process rescued over 250,000 hostages held as a human shield by the terrorists."