It was reported that Mr Letwin had been seen disposing of papers at a park close to Downing Street on five separate occasions.
Witnesses said the MP discarded more than 100 papers, including correspondence on terrorism and national security as well as constituents’ private details.
One document was said to describe how intelligence chiefs “failed to get the truth” on Britain’s involvement in controversial terrorist interrogations.
The West Dorset MP reportedly tore up the documents but did not shred them, leaving them still legible.
Pictures show the MP apparently about to drop papers into a bin while talking on a mobile phone, and in one image he appears to hand papers to a cleaner holding a bag.
The papers are said to date from July 27 2010 to September 30 2011, and include five Intelligence and Security Committee (ISC) letters.
In one, MP Andrew Tyrie reportedly tells ISC chairman Sir Malcolm Rifkind the committee “failed to get to the truth on UK involvement in rendition”.
Another discarded document refers to al Qaida links to Pakistan, the newspaper claimed.
Prime Minister David Cameron, Liberal Democrat leader Nick Clegg and Chancellor George Osborne are all said to be mentioned in the dumped papers, as are organisations including the Ministry of Defence, the Home Office and the NHS.
Mr Letwin’s actions were described as a “security breach”, but a spokesman for the minister insisted that the papers did not contain any sensitive material.
“Oliver Letwin does some of his parliamentary and constituency correspondence in the park before going to work and sometimes disposes of copies of letters there. They are not documents of a sensitive nature,” the spokesman said.
Michael Dugher, Labour’s shadow minister without portfolio, has written to Sir Gus O’Donnell calling for an investigation, to ascertain the classification of any discarded documents and whether the strict procedures for the disposal of Government documents had been breached.
Mr Dugher said he was “alarmed” to see reports that Mr Letwin had been seen “repeatedly discarding official Government documents - some said to deal with intelligence and counter-terrorism - in a bin in a central London park”.
He said: “This shows how out of touch Oliver Letwin and Conservatives really are. He and rest of the Tory-led Government are treating the public and their constituents with contempt by handling sensitive correspondence in this cavalier way.”
In the letter, Mr Dugher said: “Civil servants are subject to disciplinary procedures if the proper processes are not adhered to.
“It cannot be that there is one rule for ministers and another for everyone else.”