Ed Miliband has accused the Daily Mail of lying about his father after the newspaper headlined an article about him as "The man who hated Britain".
The Labour leader said he was "appalled" that after offering him a right of reply, the paper had repeated its original article and also now "described my father's legacy as evil".
He said it raised questions about morality and boundaries for newspapers.
The Mail says it will not apologise and stands by the story.
However, its deputy editor later said it was an "error of judgement" for the paper to have published a picture of Ralph Miliband's grave on the website version of the story, prompting the Labour leader to say the newspaper "should now apologise".
In Saturday's article, journalist Geoffrey Levy questioned how the beliefs of Ralph Miliband, a Marxist academic who died in 1994, may have influenced the Labour leader and his brother, former Foreign Secretary David Miliband.
It highlighted a diary entry Ralph Miliband wrote at the age of 17 saying that the English were "perhaps the most nationalist people in the world... you sometimes want them almost to lose [the war] to show them how things are".
The paper goes on to say "how passionately he would have approved today of his son's sinister warning about some of the policies he plans to follow if he ever becomes prime minister".
In his piece in Tuesday's edition, Ed Miliband says his father, a Jewish refugee who fled Belgium aged 16 to escape the Nazis, "loved" Britain and served in the Navy.
He says: "There is no credible argument in the article or evidence from [Ralph Miliband's] life which can remotely justify the lurid headline and its accompanying claim that it would 'disturb everyone who loves this country'."
He says Britain "was a source of hope and comfort for him, not hatred".
"Fierce debate about politics does not justify character assassination of my father, questioning the patriotism of a man who risked his life for our country in the Second World War," Mr Miliband says.
He says the diary entry described the "suspicion he found of the Continent and the French when he arrived here".
"To ignore his service and work in Britain and build an entire case about him hating our country on an adolescent diary entry is, of course, absurd."
Mr Miliband says his father joined the Navy as he "was determined to be part of the fight against the Nazis and to help his family hidden in Belgium. He was fighting for Britain."
He adds: "My father's strongly left-wing views are well known, as is the fact that I have pursued a different path and I have a different vision.
"The idea of me being part of some 'sinister' Marxist plot would have amused him and disappointed him in equal measure and for the same reason - he would have known it was ludicrously untrue. I want to make capitalism work for working people, not destroy it."
Later, in an interview with reporters, Mr Miliband said it was "perfectly legitimate" for newspapers to discuss his father's politics.
But he said: "I was appalled when I read the Daily Mail on Saturday and I saw them say he hated Britain. It's a lie."
The Daily Mail's editorial on Tuesday - published alongside Mr Miliband's response and an abridged version of the original article - is headlined "an evil legacy and why we won't apologise".
Mr Miliband said: "I'm even more appalled that they repeated that lie today and they've gone further and described my father's legacy as evil. Evil is a word reserved for particular cases and I wasn't willing to let that stand."
He added that there were "boundaries" that newspapers should adhere to.
"It's not about regulation... but it is about me saying I think morality and our approach to these things matters."
He added that his brother and mother felt the same way he did about what the newspaper had said.
The Mail's editorial said it stood by "every word" of the article.
"We do not maintain... that the iniquity of the fathers should be visited on the sons. But when a son with prime ministerial ambitions swallows his father's teachings, as the younger Miliband appears to have done, the case is different," it said.
It suggested that Mr Miliband's plans to freeze energy prices and give councils powers to purchase land from developers, and his support for press regulation backed by law, were signs of his "own Marxist values".
It later said in a statement: "We ask fair-minded people to read our editorial today. For what this episode confirms is that you cannot allow politicians anywhere near regulating the press.
"While we respect Mr Miliband's right to defend his father... it is worth stressing that Ralph Miliband wasn't an ordinary private individual but a prominent academic and author who devoted his life to promoting a Marxist dogma which caused so much misery in the world.
"He hated such British institutions as the Queen, the Church and the Army, and wanted a workers' revolution. Our readers have a right to know that."
Speaking on the BBC's Newsnight programme, Daily Mail assistant editor Jon Steafel said the picture of Ralph Miliband's grave, which included the caption "grave socialist", was removed after he personally took a call from Ed Miliband.
But he continued to defend the article and headline itself as "entirely justified".
Alastair Campbell, the former director of communications at Downing Street under Tony Blair, said the Daily Mail was "the worst of British values posing as the best" and its editor Paul Dacre should have appeared on Newsnight himself to defend the article.
A spokesman for Mr Miliband said: "We continue to believe that the article... and a subsequent article... were smears. The deputy editor of the Daily Mail showed tonight he could not justify either of them."
'Playing the ball'
Prime Minister David Cameron was asked about the row on BBC Radio 4's Today programme, but said he had not read the original article or the response from the Labour leader.
He added, though, that "if anyone had a go at my father I would want to respond vigorously" so totally "understand what Ed's done".
The prime minister later rejected any comparison between attacks by Conservative-supporting newspapers on Labour politicians and smear campaigns led by Gordon Brown's former spin doctor Damian McBride as " frankly ludicrous".
Deputy Prime Minister Nick Clegg said he supported the Labour leader, tweeting: "Politics should be about playing the ball, not the man, certainly not the man's family."
But Health Secretary Jeremy Hunt challenged Ed Miliband to distance himself from his father's views on capitalism, saying "Ralph Miliband was no friend of the free market economy... I've never heard Ed Miliband say he supports the free market economy."
In a statement, the Labour Party said: "Ed Miliband wrote his right to reply article because he wanted to state clearly that his father loved Britain.
"He wanted the Daily Mail to treat his late father's reputation fairly. Rather than acknowledge it has smeared his father... the newspaper has repeated its original claim. This simply diminishes the Daily Mail further."