Lord Justice Leveson has asked police to get to the bottom of how Milly Dowler's voicemails came to be deleted.
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 newspaper, 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.
Richard Caseby, managing editor of The Sun, accused Guardian editor Alan Rusbridger yesterday of "sexing up" his paper's coverage of the phone hacking scandal.
Justice Leveson said on Wednesday: "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 currently putting together a briefing document containing a "comprehensive" analysis of the background.
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.
He told the inquiry that the reporter asked Lewis in reference to the family's STG2 million ($A3 million) phone hacking settlement with News International: "Will the Dowlers be giving their money back?"
Sherborne said he had referred the matter to the Press Complaints Commission.
Jonathan Caplan QC, counsel for the Daily Mail's publishers, Associated Newspapers, stressed that the reporter was not attacking the Dowlers.
"He was making a proper approach to Mr Lewis as their solicitor, trying to see what the implications might be from recent reports concerning deletion of Milly Dowler's voicemails, no more than that," he told the inquiry.
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