Forty-six eminent figures including military men, ex-diplomats and bishops have written to Tony Blair urging an inquiry into civilian deaths in Iraq.
The Lancet claimed Iraqis are now 58 times more likely to die a violent death
A study in a medical journal said nearly 100,000 died after the invasion. Other groups put the figure at 15,000.
Mr Blair told MPs the most accurate estimate - of between 3,853 and 15,517 for April to October this year - was from the Iraqi Ministry of Health.
And he argued terrorists, not US-led troops were to blame for the deaths.
At prime minister's questions, Mr Blair said he did not accept the casualties' inquiry was needed for the UK to fulfil its international obligations.
He urged people to back efforts to hold elections in Iraq in January.
"Those people that are killing innocent people in Iraq today, who are responsible for innocent people dying, are the terrorists and insurgents who want to stop the elections happening in Iraq," he said.
"Any action that the multi-national force or the Iraqi people are taking in Iraq is in order to defeat those people who are ... killing anyone who wants to make the country better."
The publication of the letter to Mr Blair marks the launch of a new campaign by health charity Medact and the Iraq Body Count project.
Names on the letter include retired General Sir Hugh Beech, the bishop of Coventry and an ex-ambassador to Iraq.
It also includes the former assistant chief of the defence staff Lord Garden, now a Liberal Democrat peer, and playwright Harold Pinter.
VARYING IRAQ DEATH ESTIMATES
Iraq Body Count:
14,000-16,800 since March 2003
Iraq-based People's Kifah:
27,000 March-October 2003
US-based Brookings Institute:
Up to 27,000 to August 2004
Foreign Secretary Jack Straw
10,000 to March 2004
100,000 since March 2003
The letter urges Mr Blair to set up an independent inquiry to establish just how many people have been killed or injured in Iraq, along with reasons for the casualties.
Lord Garden told BBC News: "We have taken it [Iraq] over and we are going to try and make it a democratic country.
"We need to show the rest of the world that we are doing it in a proper, legal, moral way and one that can get the hearts and minds of the Arab and Muslim world.
"If we appear to be discarding the people there and saying they are not really important we are going to lose that battle."
'Make an effort'
Human rights campaigner Bianca Jagger, who is also a signatory, said: "Since they don't want to catalogue the deaths, they are giving the impression that ordinary
Iraqi lives are worth less than those of the soldiers and that life is expendable.
"No figures in a war zone are going to be perfect - but that's no excuse for not trying."
The letter says: "As you know, your government is obliged under international humanitarian law to protect the civilian population during military operations in Iraq, and you have consistently promised to do so.
"However, without counting the dead and injured, no-one can know whether Britain and its coalition partners are meeting these obligations."
The letter's publication marks the launch of a new campaign by health charity Medact and the Iraq Body Count project challenging the government to count casualties.
Medact director Mike Rawson said: "We need casualty estimates to assess the effect of weaponry on the population and to plan health care for the injured.
Without information, everyone is working in the dark."
He argued the Iraqi health system should not be left to keep a tally on its own and he argued the US-led coalition had a responsibility to "commission and resource this work themselves".