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Scotland Yard Commissioner Bernard Hogan-Howe says the review of Gareth Williams 'spy in bag' case is considering conducting voluntary mass DNA testing MI6 officials.
The papers say that 15 members of the security service have already provided samples.
There was one source of unidentified DNA found in Mr Williams flat.
On Gareth Williams an MI6 spokesman said: "At no time did we withhold any evidence".
This is the first time such a spokesman has been quoted as MI6.
The Metropolitan Police's Deputy Assistant Commissioner Martin Hewitt said they are trying to "trace unidentified DNA" to understand what happened to Gareth Williams.
He added that the case "remains a current investigation".
Following an inquest, a coroner can return a 'narrative verdict'. This is a factual statement of the circumstances surrounding someone's death, without attributing the cause to an individual. Narrative verdicts have been an option for coroners in England and Wales since 2004.
DCI Jackie Sebire has said that new lines of inquiry had come to light during Gareth Williams' inquest and that the investigation into his death is continuing.
In a statement delivered by solicitor Robyn Williams, the family of Gareth Williams said their grief was exacerbated by the failure of Gareth's employers, MI6.
Speaking on behalf of the Williams family, solicitor Robyn Williams said: "Our grief is exacerbated by the failure of his employers at MI6 to take even the most basic inquiries as to his whereabouts and welfare, which any reasonable employer would have taken."
He said the Williams family were "extremely disappointed" over the failure of MI6 to make relevant information available and asked for the Metropolitan Police to review how the investigation will proceed.
He added: "Gareth always was and always will be a special and adored son and brother.
"We miss him every single day and cannot describe the depth of the sorrow his absence leaves in our lives. We love you Gareth and will treasure your memory eternally. To live on in the hearts of those we love and leave behind is not to die."
One of Britain's most senior spies apologised to Gareth Williams' family today for the mix-up which saw MI6 fail to report his disappearance for a week.
Sir John Sawers, chief of the Secret Intelligence Service, expressed the "deepest condolences" of MI6 and GCHQ for the death.
In a statement delivered by MI6 lawyer Andrew O'Connor, Sir John said the service should have acted more swiftly when Mr Williams failed to turn up to work in August 2010.
Mr O'Connor said: "On behalf of the whole organisation, Sir John regrets this deeply and apologises unreservedly."
Latest ITV News reports
Police investigating the death of MI6 code-breaker Gareth Williams are to intensify their inquiries into his colleagues and work.
Whatever the coroner's verdict today at the inquest into the death of MI6 spy Gareth Williams, many questions will remain unanswered.