The question of how Milly Dowler's voicemail came to be deleted has achieved such significance that it "cannot be left alone", the chairman of the press standards inquiry has said.
A lawyer for Scotland Yard said this week it was "unlikely" that News International journalists erased messages from the schoolgirl's phone three days after she went missing in 2002.
The revelation prompted criticism of the Guardian, which reported in July that the News of the World had deleted voicemails from 13-year-old Milly's phone to make room for new ones, giving her parents false hope she was still alive.
On Tuesday, Richard Caseby, managing editor of the Sun, accused Guardian editor Alan Rusbridger of "sexing up" his paper's coverage of the phone-hacking scandal.
Lord Justice Leveson, who is chairing the public inquiry into press standards, said it was "likely to be in the public interest" for the matter to be cleared up in an "orderly manner". He said it would primarily be for the police to provide further details of what really happened.
Addressing Scotland Yard's barrister, Lord Justice Leveson said: "I am sure they will also see the value in preventing a continual dialogue of allegation, counter-allegation, suggestion, inference.
"It is absolutely open to you, if you wish, to express a concern about the impact on your ongoing investigation.
"My present view is that this has achieved such a significance that it cannot be left alone, and that although obviously I do not want to prejudice any investigation that is ongoing, I think doing nothing is probably not an option."
Neil Garnham QC, counsel for the Metropolitan Police, said officers were in the process of putting together a briefing document containing as "comprehensive an analysis of the background" as possible.
David Sherborne, representing Milly's family, complained that a journalist from the Daily Mail's Ephraim Hardcastle column contacted the Dowlers' solicitor, Mark Lewis, on Tuesday.