The documents were left on a commuter train on Tuesday morning by a member of the Joint Intelligence Committee assessment staff.
Updating MPs on the situation, Mr Miliband said the official - who has been suspended - had no authorisation to remove the files from Government premises.
Former Permanent Secretary for Security and Intelligence Sir David Omand will carry out a full investigation of the circumstances of the case, Mr Miliband added.
However there was no evidence to suggest vital national security interests had been damaged, or that any individuals or operations were at risk.
Tory spokesman Francis Maude said: "There can scarcely have been a graver breach of intelligence and security procedures than this."
The documents, containing an assessment of al Qaida's vulnerabilities and the competence of Iraqi security forces, were handed to the BBC.
Mr Miliband said: "While the documents do not contain the names of individual sources or specific operational details, they are sensitive, high-level intelligence assessments."
The official told superiors about the loss of the documents yesterday morning and the BBC subsequently handed them over.
Mr Miliband said: "There is no evidence to suggest that our vital national security interests have been damaged or any individuals or operations have been put at risk.
"However the police investigation is continuing."
He added: "This was a clear breach of well established security rules which forbid the removal of documents of this kind outside secure Government premises without clear authorisation and compliance with special security procedures."
In this case, "no authorisation was sought for the removal of the documents" and the official has been suspended as part of a standard civil service disciplinary procedure.
All Joint Intelligence Committee staff have been reminded of the rules, as have officials in other Whitehall departments with access to sensitive material.
"It is a matter of utmost concern to the Government that this breach of security has happened," Mr Miliband said.
Mr Maude said: "The Prime Minister said yesterday: 'We should take no risks with national security'.
"There can be few greater risks that the casual abandonment of top secret intelligence material on a train."
He added: "That al Qaida do not today know precisely what Britain know about their activities, and perhaps more importantly what Britain doesn't know about their activities, is entirely due to the responsible way in which the BBC has behaved and reflects no credit whatsoever on the Government."
It was, he said, a "lamentable lapse of basic security awareness and procedures".
Mr Maude said there was "clearly a major systemic problem with data security at the heart of the Government."
He asked "what reason could there possibly be" for allowing an official to remove such sensitive files.
"Why, now that such powerful encryption is available, why are documents at this extremely high level of security, why are they printed onto paper at all?
"Will anybody and it may be too early to say this, will anybody be prosecuted under the Official Secrets Act?"
Mr Maude suggested the lapse had come after a raft of other data security breaches in previous months.
He went on to suggest there was a "real issue with civil service morale which leads to laxity in the way in which procedures are not complied with".
Mr Maude said Mr Miliband was responsible for information security across the whole of Government.
"There is no evidence that he takes this crucial part of his responsibilities nearly seriously enough."
Mr Miliband told Mr Maude the copies of the documents that were returned were the original copies. "Obviously the police will be investigating the question of these originals and looking into any circumstances surrounding these original copies and how they found their way from being lost on the train on Tuesday to the BBC."
He went on: "This is a clear breach not just of the rules, the rules that people sign up to when they work in the assessment staff."
He said he would not comment on potential prosecutions.
Mr Miliband said there were "clear rules" for staff. "This is a case where those rules weren't followed and it is a matter of deep regret that those rules were not followed."
He rejected Mr Maude's claim that morale was low. They did an "extraordinary job".
"I don't believe that is the reason why this document was left on a train."
Labour former minister Don Touhig (Islwyn) said: "MPs in this House who serve on the Intelligence and Security Committee have to go to the Cabinet Office and read the documents there.
"They may not be removed. Why on earth does someone who works in the Cabinet Office need to remove documents at all?"
Mr Miliband said: "There are circumstances where people need to have meetings outside secure premises and they need to be transferred from one place to another. There are the most stringent rules in place for that."
For the Liberal Democrats, Susan Kramer said she hoped the investigators did not dismiss as "simply chance or accident" the fact the documents could have been seen by others.
She asked for clarification on the procedures regarding officials taking away secret documents. "Just a locked box for example doesn't seem terribly appropriate."
She was "concerned" that the whole incident should not be "slur" on the civil service as a whole.
"We certainly don't need to treat this as suggesting in any way that the civil service at large is not conscious of the issues.
"But I do indeed wish the issue of culture be fundamentally addressed."
Mr Miliband said it was "easy" in such circumstances to criticise the civil service generally.
On the rules for taking documents away from buildings he said: "There was no authorisation for this document to be taken out of the building. The rules were absolutely clear - authorisation should be sought.
"If a document is taken out of the building it should only be in the most exceptional circumstances."
Tory Julian Lewis (New Forest E) called for officials to be searched when they left the Cabinet Office "to see that they are not removing classified material" and suggested senior staff might think they were "above such procedures".
Mr Miliband said: "Searching each individual from the assessment staff who left the building each evening would clearly be quite an onerous task. But Sir David will look at all suggestions."
Chairman of the Home Affairs Select Committee Labour's Keith Vaz said: "Many of us have been campaigning for many years for more transparency, but this of course is not what we had in mind." He called for the inquiry to be published "so we can see whether the process was followed".
Tory Douglas Hogg (Sleaford and N Hykeham), a former Foreign Office minister, said: "I wouldn't have favoured being searched when I left the Foreign Office." He said there was a "pattern of failure" and mistakes on security lapses were not being addressed.
Mr Miliband said: "This is one individual within the assessment staff." But the Minister did recognise the "gravity" of the issue.
Labour's Andrew Mackinlay (Thurrock) blamed the loss on a seconded MI5 officer and expressed "no confidence" in Sir David's inquiry, which would be a "cover-up".
Mr Mackinlay, a member of the foreign affairs select committee, said: "Isn't it a fact that this official was actually a seconded MI5 officer."
He told Mr Miliband: "Although you are innocent of responsibility for this cock-up, nevertheless you are responsible for looking at the investigation and the remedy.
"I have no confidence whatsoever in Sir David Omand. He's a safe pair of hands and will be involved in a cover-up."
Mr Mackinlay called for proper parliamentary oversight of the security and intelligence services.
Mr Miliband said Mr Mackinlay had strong views about the status of the intelligence and security committee.
"On the question of the status of the individual concerned, I'm not going to get into a discussion of his particular status. I don't think it is fair to the individual apart from anything else.
"As for your comments about Sir David Omand, I met him this morning. He's determined to do a rigorous investigation to make sure we, as far as possible, have the necessary safeguards in place."
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