The Press Complaints Commission has revealed it has so far received 726 complaints about the Daily Mail's coverage on Ralph Miliband, the Labour leader's father.
The figures came after Ed Miliband wrote to the newspaper's owner, Lord Rothermere, complaining that a Mail on Sunday journalist had broken into a private family memorial to ask about the legacy of Ralph Miliband.
Ed Miliband wrote: "Sending a reporter to my late uncle's memorial crosses a line of common decency. I believe it a symptom of the culture and practices of both the Daily Mail and the Mail on Sunday."
Geordie Greig, the editor of the Mail on Sunday, has "unreservedly" apologised for the incident, saying it was a "terrible lapse of judgment" and that two journalists on the paper have been suspended.
The chair of the Press Complaints Commission, Lord Hunt, said the PCC would "follow this matter closely".
"We would, of course, take forward a complaint from the Miliband family, should we receive one."
The Mail's coverage of Ed Miliband's father, a Marxist academic, has drawn widespread criticism.
Alastair Campbell has also started a petition, challenging Daily Mail editor Paul Dacre to a live TV debate.