Ed Miliband has claimed the Daily Mail's attack on his father and the Mail on Sunday's gatecrashing of a private family memorial service for his uncle are a symptom of the culture at the titles.
In the latest salvo in the bitter row between the Labour leader and the newspapers, Mr Miliband said he did not believe the actions could be blamed on "rogue" reporters or editors.
Labour said Viscount Rothermere, chairman of the company which owns the newspapers, had apologised after a Mail on Sunday reporter turned up uninvited to an event commemorating Mr Miliband's uncle.
But in Lord Rothermere's reply to a letter from Mr Miliband he said he did not believe the incident reflected the culture and practices of the Daily Mail or Mail on Sunday.
The row was sparked by an article in Saturday's edition of the Daily Mail accusing Mr Miliband's late father Ralph, a Marxist academic, of "hating Britain".
Mr Miliband told the LabourList website he felt an "apprehension" before speaking out about the treatment of his father but it was the right thing to do.
He added: "It's the first time this has happened to me in this way, but many other people have been affected by this sort of practice and I'm serious about what I said in my letter to Lord Rothermere: he's got to look into the culture and practice of the Mail and the Mail on Sunday.
"What we've seen over the past five days is a symptom of that and it's time he took a long hard look at the way his papers are run because I don't believe that reflects the values of the British people.
"I want to know how these practices are allowed to happen. Not on the basis of being 'one rogue reporter' or 'one rogue editor' but what is it about the culture and practice of the organisation that makes these kind of things acceptable? Because the decisions made by an individual in an organisation are shaped by the culture and practice of an organisation."
Mr Miliband was given the right to reply to the Daily Mail's essay on his father, who died in 1994, but the newspaper accompanied his piece on Tuesday with an editorial accusing the left-wing thinker of leaving an "evil legacy".
The Labour leader said: "I t has been hard because this is about my family and it's not a fight I picked. The Mail did that and I had to speak out to defend my Dad and to stand up for a better kind of political debate so the next election isn't fought in the gutter.
"On Monday night I was thinking about the article I'd written and - I don't normally feel these kind of things - but I felt a sense of apprehension about it. I didn't know they were going to compound the problem by describing my Dad's legacy as 'evil' but even then I knew that even though I didn't want to be in this position it was the right thing to do.
"You've got to draw the line somewhere. I thought it was right to speak out."
Mr Miliband acknowledged that the row "certainly hasn't improved our relationship" with the Daily Mail.
"But you can't judge these things on the basis of 'how are we going to get favourable coverage?'
"You've got to judge them on the basis of doing the right thing, and that's what I thought in relation to what the Daily Mail did in smearing my Dad and that's what I thought in relation to the Mail on Sunday sending a reporter to my uncle's memorial.
"I did face a choice but I decided I couldn't remain quiet and hope it goes away in the way politicians are supposed to do."
Both Lord Rothermere and Mail on Sunday editor Geordie Greig apologised to Mr Miliband after a reporter attended a memorial service for his late uncle Professor Harry Keen, being held on the 29th floor of Guy's Hospital in central London.
A Labour spokesman said: "Lord Rothermere has repeated the apology for the behaviour of the Mail on Sunday. This is an important step.
"However, he says he does not believe it reflected the culture and practices of the Mail or Mail on Sunday, and also he does not address the treatment of Ed Miliband's dad over the last few days.
"We continue to believe these issues need addressing and until they do so, many people will continue to believe that these newspapers are not upholding the values and decency of the British people."
Mr Greig apologised unreservedly and said that two journalists on his paper had been suspended pending a full investigation into what he said was "a terrible lapse of judgment".
He added: "It is completely contrary to the values and editorial standards of The Mail on Sunday."
Earlier, Deputy Prime Minister Nick Clegg launched an outspoken attack on the Daily Mail, accusing the paper of "overflowing with bile" about modern Britain, and said Mr Miliband's response was "quite understandable".
"When I heard the Daily Mail accusing someone of saying that they didn't like Britain... I'm not a regular reader of this newspaper but every time I do open it, it just seems to be overflowing with bile about modern Britain," he said on his weekly radio phone-in on LBC 97.3.
"They don't like working mothers, they don't like the BBC, they don't like members of the royal family, they don't like teachers, they don't like the English football team - the list goes on," he said.
"It seems to me that if anyone excels in denigrating and often vilifying a lot about modern Britain, it's the Daily Mail."
Mr Clegg is the latest senior figure from across the political spectrum to voice concern at the way the Mail portrayed the Labour leader's father, who was a Jewish refugee who fled to Britain to escape the Nazis and served in the Royal Navy in the Second World War.
Mr Miliband said he wanted "proper standards of decency" in the press as he sought to return to his campaign h ighlighting the rising cost of living.
" I want this next election to be about the cost of living not about smears on my late father," he told LabourList.
"That is why I chose to speak out now because the British people need a debate about the issues which matter to them and that won't be possible if this kind of character assassination of people's families continues."
He added: "If we're going to have those massive debates about the cost of living, we need to have proper standards of decency in our press."