The Prime Minister said he understood the concerns raised about the missing file which was handed to then home secretary Leon Brittan by the Conservative MP Geoffrey Dickens.
"That's why I've asked the permanent secretary at the Home Office (Mark Sedwill) to do everything he can to find answers to all of these questions and to make sure we can reassure people about these events," he said.
"So it's right that these investigations are made. We mustn't do anything, of course, that could prejudice or prevent proper action by the police. If anyone has information about criminal wrong-doing they should, of course, give it to the police."
Mr Sedwill has already commissioned one review into what happened to the dossier, after concerns were raised last year in Parliament and the media, which found it had not been retained "in line with departmental policy".
The review concluded the Home Office "acted appropriately, referring information received during this period to the relevant authorities".
Reports yesterday suggested the file included the name of a former Tory MP who was found with child pornography videos at UK customs in the 1980s but escaped without any action being taken. The Customs officer is said to have spoken to detectives on Operation Fernbridge, an investigation into allegations of sexual abuse by people including high-profile figures in London.
Labour MP Tom Watson said he was writing to DPP Alison Saunders to ask her to examine the evidence relating to the unnamed Tory politician. He said: "It's a remarkable revelation. If true, it shows that a crime was not investigated but also is shocking because it's yet another example of intelligence going missing.
"I hope the DPP will share the concern of many MPs about this."
The Metropolitan Police said: "We are not prepared to give a running commentary on Operation Fernbridge."
Meanwhile, it emerged that four more cases of historic sex abuse have been referred to the police by Home Office officials in recent months, following a review ordered last year covering the period 1979 and 1999.
A review of a database containing details of 746,000 files identified 13 items of information about alleged child abuse, including four cases involving Home Office staff.
Nine of these items, including all cases involving Home Office officials, were already known to the police or were reported to them by the Home Office at the time. The remaining four have now been passed to the police for a "proper assessment".