The Guardian has corrected 26 articles alleging that the News of the World gave Milly Dowler's parents false hope by deleting her voicemails.
A lawyer for Scotland Yard told the Leveson Inquiry last week it was "unlikely" News International journalists erased messages from the schoolgirl's phone three days after she went missing in 2002.
The Guardian published a correction to its original story from July 5 which first made the allegation.
This has also been added to the bottom of the online versions of about 20 later articles which repeated the claim.
Richard Caseby, managing editor of The Sun, wrote to the Guardian's editor, Alan Rusbridger, and its readers' editor, Chris Elliott, on Friday asking for corrections in print and on the paper's website of 26 articles published since the first story.
Mr Caseby said on Sunday: "Alan Rusbridger has corrected the gross inaccuracy of his original statement of fact that the News of the World deleted the voicemail of Milly Dowler and gave her parents false hope she was alive.
"However, that statement of fact was repeated in 26 subsequent Guardian articles and the record now needs to be corrected with respect to those, both in print and online."
The Guardian, in its corrections and clarifications column, today said it had now added a footnote to 37 stories online that contain either the error or reference to it.
Lord Justice Leveson, who is chairing the public inquiry into press standards, has asked police to get to the bottom of how Milly's voicemails came to be deleted.
"My present view is that this has achieved such a significance that it cannot be left alone," he said at a hearing last week.