Mr Straw also promised more openness about the security services, and an announcement before the summer on how they might be opened up to greater public scrutiny.
In a Commons debate, he also said he would never allow a minister or MP to demand a file on him be destroyed. There had been reports that Peter Mandelson, the Minister Without Portfolio, wanted records of his activities in the Young Communist League removed from the archives.
Mr Straw also suggested that security vetting of ministers would not have led to disclosure of old information from the Cold War period because it would no longer be "live" and would not routinely be consulted. A file was held on him when he was president of the National Union of Students between 1969 and 1971.
Responding to questions from Julian Lewis, the Conservative MP for New Forest East, Mr Straw said the security services had a duty to "protect national security from actions intended to overthrow or undermine democracy by political, industrial or violent means."
"Our Parliamentary democracy is not currently threatened by the activities of subversive groups ... the limited resources which the service actually devotes to counter subversion are focused on monitoring so it would be able to respond if a threat should emerge," he said.
Although the nature of the security services' work required protection from "the full glare of publicity," he planned to look at ways of opening them up a little. For example, MPs might be told how many files on individuals were currently "live."
Since 1992, files no longer needed had been destroyed as resources allowed. This process had been speeded up recently but there was no question of allowing ministers to ask for their files to be shredded. "It would be very wrong to do so in respect of private individuals, it would be even more wrong to do so at the behest of honourable or right honourable members and particularly for ministers," he said.
Mr Lewis had complained that the destruction of files might deprive historians of material, for example relating to Nazi sympathiser groups in Britain in the Second World War.