Ministers were warned three months ago the police were having problems tracing hundreds of dangerous British criminals convicted overseas, it has emerged.
Mr Reid said the matter was a "very serious problem"
Of 27,500 criminals, police say 540 were serious offenders - including rapists, paedophiles and murderers. So far, just 260 have been identified.
There is concern offenders could have been cleared to work with children.
Earlier, the Home Office was accused of ignoring files on the offenders. The home secretary promised a full inquiry.
'Lack of clarity'
Initially Joan Ryan, the minister responsible for the Criminal Records Bureau, said ministers had not been aware of the issue until this week.
But the Association of Chief Police Officers (Acpo) revealed they wrote to police minister Tony McNulty in October.
The letter complained that information supplied by foreign authorities was not clear enough to put into the Police National Computer (PNC) - but did not mention the backlog of 27,000 cases.
In a separate letter in the same month, Acpo requested more money to help them deal with the backlog.
The Home Office said Ms Ryan had dealt with the first letter, while the request for more funds was deal with by an official, not a minister.
The department still insists no minister was aware of the backlog in cases until this week.
Shadow home secretary David Davis said the position of the two ministers would be "untenable" if they knew of the problems with the offenders' details.
"We need to see the full copy of this letter. Acpo should now publish it including all replies," he said.
Mr Reid has said he will probably publish the letter - and replies to it - at the end of the inquiry.
BBC political editor Nick Robinson said Acpo was saying the letter had highlighted difficulties with the procedure, while Mr Reid was saying the letter had largely praised the new system.
Our political editor said Mr Reid described the opposition's attempt to get the letter published as "mischief-making".
'Catalogue of blunders'
In March 2006 Acpo took over responsibility for logging the cases with the police database.
On Tuesday, Acpo's Paul Kernaghan told a Commons committee that details of 27,529 cases, including 25 Britons convicted of rape, had been "left in box files" at the Home Office before his team had taken over.
The cases involved included:
25 rapes3 attempted rapes29 paedophiles17 other sex offenders5 murders9 attempted murders13 manslaughter convictions29 robberies
He said Acpo was now working through the backlog.
Mr Reid made a statement to the Commons on Wednesday saying that the details of 260 of the 540 serious criminals had now been entered into the PNC.
"The remaining 280 cannot be entered on the computer and are the subject of further inquiries to the notifying country to get more details to try to establish the identity of the offender," he added.
An inquiry into the Home Office's handling of the details was expected to be completed within six weeks, Mr Reid said.
Mr Davis attacked the department's recent record as a "catalogue of blunders".
"The last three years have been the worst three years in the Home Office's 200-year history," he said.
The Liberal Democrats also criticised the government, saying the mixture of "ignorance and incompetence would be comic if it did not jeopardise public safety in the way that it has".
Earlier, Tony Blair and Conservative leader David Cameron had clashed over the issue in a heated Prime Minister's Questions.