Lord Justice Leveson has told his inquiry into media ethics he believes police should clear up who was responsible for deleting Milly Dowler's voicemails.
The inquiry chief said: "My present view is that this has achieved such a significance that it cannot be left alone... I think doing nothing is probably not an option."
It had been thought the NOTW deleted the messages while Milly was missing - an act that led to her parents being given false hope.
But it has since emerged that they were probably deleted automatically by the phone system, 72 hours after they were listened to.
It was the revelation that Milly's phone had been hacked that took the hacking scandal to a new level and precipitated the Sunday tabloid's closure.
Neil Garnham QC, counsel for the Metropolitan Police, says officers are putting together a briefing document containing as "comprehensive an analysis of the background" as possible.
The inquiry was told that journalist from the Daily Mail's Ephraim Hardcastle column contacted the Dowler family's lawyer on Monday.
The reporter had asked if the Dowlers would be giving back the £2m paid out by News International after new details suggested the NOTW did not delete Milly's messages, it heard.
Their barrister David Sherborne said he had referred the matter to the Press Complaints Commission.
Lord Justice Leveson's intervention came as former NOTW legal manager Tom Crone continued to give evidence to the inquiry.
On Tuesday, Mr Crone said he had given advice on phone hacking as early as 2004, two years before former Royal editor Clive Goodman was arrested.