The Daily Mail is under fire after it refused to apologise to Ed Miliband over an article that labelled his late father "the man who hated Britain".

The paper prompted an angry stream of reaction on Tuesday morning when it stood by the profile published on Saturday, which said the beliefs of Ralph Miliband "should disturb everyone who loves this country".

The Mail agreed to print a right of reply by the Labour leader, but ran it alongside an abridged version of the original article and a trenchant 1,000-word editorial headlined "An evil legacy and why we won't apologise".

David Cameron and Nick Clegg waded into the row on Tuesday, backing Miliband's response. Cameron said he had not read the original article but said that "if anyone had a go at my father, I would want to respond vigorously".

Clegg wrote on Twitter: "I support Ed Miliband defending his dad. Politics should be about playing the ball, not the man, certainly not the man's family."

The former Labour MP David Miliband tweeted: "My dad loved Britain. Here's the truth," and linked to his brother's article defending their father, who fled Belgium aged 16 to escape the Nazis.

Ed Miliband wrote in the Mail: "There is no credible argument in the article or evidence from his life which can remotely justify the lurid headline and its accompanying claim that it would 'disturb everyone who loves this country'."

Critics of the Mail highlighted the paper's stance on Oswald Mosley's British Union of Fascists in the 1930s. Lord Prescott, the former deputy prime minister, posted a picture of a Daily Mail article by Viscount Rothermere published eight decades ago headlined "Hurrah for the Blackshirts", and said: "Here's a Daily Mail leader praising fascists written by the great-grandfather of the paper's current owner."

The Bradford West MP George Galloway said: "How low can the Daily Mail sink? How about its despicable smear on Jewish refugee from Nazism and D-Day vet Ralph Miliband? The Daily Mail which supported fascism and ran a front page splash in support of British Nazis titled 'Hurrah for the Blackshirts!'"

Raymond Snoddy, the prominent media commentator, said the Mail owed Miliband an apology for its latest attack. "Daily Mail really hasn't sustained the case that Miliband snr was The Man Who Hated Britain merely Marxist class warrior. An apology is due," he tweeted.

Owen Jones, the Independent columnist and socialist commentator, said: "Weirdly compelling how all the worst elements of our country – fear, prejudice, hate – have been stuffed into paper form, aka the Daily Mail."

The Labour MP Paul Farrelly said the Mail's "disgraceful smear" was linked to Ed Miliband's backing of an independent press watchdog that would limit the involvement of newspaper owners.

"The Daily Mail continues to plumb new depths in its attacks on both Labour and Ed Miliband, he said. "People should be under no illusion that this campaign of intimidation is not just political, but highly personal – because Ed has come out strongly for a truly independent press watchdog, not controlled by the likes of Mail editor Paul Dacre.

"This disgraceful smear of Ed's dead father shows once again what a mockery it is for the Mail's editor to have overseen the code on standards at the discredited Press Complaints Commission. The sooner our media moves on from this sort of behaviour, the better."

Insiders at the Mail refused to be drawn into the row on Tuesday morning, conceding only that it was "a fairly unique situation" and that the paper had made clear its views.

"It's unusual but all the answers are in today's piece. The Mail has put in the paper how it feels about it," said one source.