Conservative claims that senior officials were involved in the loss of 25 million child benefit records have been challenged by the Treasury.
The government has insisted the security breach followed a junior member of staff breaking the rules.
The loss of the HM Revenue and Customs computer discs may have put members of the public at risk of identity fraud.
The Treasury said aspects of the Conservatives' account of events were factually inaccurate.
It is understood that one worker, a 23-year-old man, has resigned over the disappearance of the two data CDs.
The Conservative head of the Public Accounts Committee, Edward Leigh, claims senior Revenue and Customs officials approved the release of detailed information to the National Audit Office (NAO).
He said the NAO wanted only limited child benefit records but was told in an e-mail from a senior business manager in March that to remove more sensitive information was too costly and complex.
That e-mail was apparently copied to an assistant director of the department.
The result was that full details were sent to the audit office at that time, and again in October when they were lost in internal post.
The Treasury has challenged aspects of the account but refuses to elaborate.
Shadow chancellor George Osborne said Prime Minister Gordon Brown's account of what happened had been undermined.
"This was systemic failure, not individual error by a junior official," he said.
MISSING DATA INCLUDES
National insurance number
Name, address and birth date
Names, sex and age of children
Bank/savings account details
"Gordon Brown needs to tell us the whole truth of why the security of all families in the country has been put at risk."
During a heated prime minister's questions session, Mr Brown told MPs: "I profoundly regret and apologise for the inconvenience and worries that have been caused to millions of families who receive child benefits.
"When mistakes happen in enforcing procedures, we have a duty to do everything we can to protect the public."
He said he had ordered a review by the Cabinet Secretary of data safety in government and would give Information Commissioner Richard Thomas the power to spot check departments to ensure data was safe.
Conservative leader David Cameron said people would "be angry that the government has failed in its first duty to protect the public".
Mr Cameron said people were "desperately worried" and they would "find it frankly weird" that Mr Brown still wanted to go ahead with plans for a national ID cards scheme and register.
Two Labour backbench MPs - Karen Buck and Andy Love - said the government should "pause" and "stand back" from the planned project.
The entire child benefit database was sent via internal mail from HMRC in Washington, Tyne and Wear, to the NAO in London via courier TNT on 18 October.
The data on the two missing discs includes names, dates of birth, bank and address details.
CHILD BENEFIT HOAXES
Hours after the blunder emerged, a website claimed to be offering the missing data for download
Fullreleases.com, a site registered in Arizona, lists several files entitled "child benefit", but users must pay $29.95 plus tax to join before they can view them
However, once money is paid the files cannot be accessed and the site appears to be a scam
The HMRC said people should take care with any transaction on the internet and should ring its helpline if they have problems receiving child benefit
Chancellor Alistair Darling said the civil servant had broken the rules by downloading the data to disc and sending it by unrecorded delivery.
Mr Leigh said that a copy he had been given of a briefing note, written by NAO head Sir John Bourn for the chancellor, suggested that senior HMRC officials authorised the release of the sensitive information.
Bosses at the Revenue were not told about the loss of the discs until 8 November, and Mr Darling and Mr Brown learned about the situation on 10 November.
The officials involved waited before informing their superiors in the hope that the discs would be found.
The Metropolitan Police is leading the search for the discs, and the Independent Police Complaints Commission, which oversees the HMRC, is investigating the security breach.
Her Majesty's Revenue and Customs has set up a Child Benefit Helpline on 0845 302 1444 for customers who want more details.
LOST CDS - SEQUENCE OF EVENTS
18 October - Junior official from HMRC in Washington, Tyne and Wear, sends two CDs containing password-protected records to audit office in London through courier TNT, neither recorded nor registered
24 October - When package fails to arrive, second one is sent by registered post and arrives safely
3 November - Senior managers are told first package has been lost
10 November - Prime minister and other ministers are informed
12 November - HMRC tell ministers CDs will probably be found
14 November - When HMRC searches fail, Metropolitan Police are called in
15 November- Richard Thomas, Information Commissioner, says remedial action must be taken before public is informed
20 November - HMRC Chairman Paul Gray resigns; Chancellor Alistair Darling makes announcement to House of Commons