Ed Miliband has apologised for any offence caused after he posed with a copy of the Sun newspaper.
The Labour leader was pictured holding a special edition of the paper which was sent to millions of homes free to mark the start of the World Cup.
Labour MPs have criticised their leader for associating himself with the paper, which has long been criticised for its reporting of the Hillsborough disaster.
Mr Miliband said he "understood the anger" felt on Merseyside about it.
Groups representing victims and survivors of the 1989 tragedy expressed anger at Mr Miliband's actions, one describing them as an "absolute disgrace".
And a Labour councillor in Liverpool, Martin Cummins, has resigned from the party, suggesting Mr Miliband had "listened to unwise counsel in associating himself, and our party, with this degrading publication".
Mr Cummins said: "Seeing Ed promoting the Sun has rocked me to my core."
The Labour leader insisted that he had participated in the photo shoot to show his support for the England football team.
In a statement, a spokesman for the Labour leader said: "Ed Miliband was promoting England's bid to win the World Cup and is proud to do so.
"But he understands the anger that is felt towards the Sun over Hillsborough by many people in Merseyside and he is sorry to those who feel offended."
Mr Miliband, David Cameron and Nick Clegg all posed with copies of the Sun.
A Sun spokesman said: "The Sun wants to thank Ed Miliband for having his picture taken and cheering on England to #DoUsProud in Brazil.
"The free edition of The Sun is an unashamedly positive celebration of Englishness, and it should come as no surprise that politicians on all sides are happy to get behind our uplifting message."
The move has caused anger in Liverpool, at a time when inquests are being held into the deaths of 96 Liverpool football supporters at Hillsborough in 1989.
Analysis by political correspondent Chris Mason
Was it a mistake for Ed Miliband to pose for a photo, complete with a smile and a copy of The Sun?
From his perspective, here's the plus side: The Sun is the country's biggest selling newspaper, and this wasn't just an ordinary edition of the paper.
It was being sent free to millions of homes across England.
As a political leader, would you want to miss the chance to look like you're getting in the World Cup spirit?
On the downside, don't underestimate the deep seated anger with The Sun on Merseyside or the depth or longevity of Labour support there.
The question is: did the downsides even cross Team Miliband's mind?
They're not saying - but do point out the Labour leader has written for The Sun before, and will do again.
The Sun has long been scorned in Liverpool for its coverage of the tragedy, after which it criticised the behaviour of Liverpool fans, suggesting they had robbed and urinated on victims and attacked police officers attending to the injured.
In 2012, it published a "profound" apology for what it said was an "inaccurate and offensive" report.
Steve Rotheram, MP for Liverpool Walton, said he and some of his colleagues had met Mr Miliband on Thursday to discuss the matter.
"He never meant any offence, but in my opinion it shouldn't have happened in the first place," he tweeted.
The Labour mayor of Liverpool, Joe Anderson, said many people would feel "insulted" by Mr Miliband's actions.
"Like everybody in this city I am really hurt and offended by Ed Miliband's support for The Sun newspaper," he said. "Such clear support for that publication at any time would be wrong but at such a sensitive time is deeply shocking."
"For the leader of the Labour Party to make such an offensive gesture insults not only me but every person in the city.
"This is just another example of how out of touch the politicians in their ivory towers are from the lives of ordinary people."
Writing on Labour list, Labour MP Tom Watson suggested the Labour leader had been "hoodwinked" by the newspaper.
"Scouse friends with accompanying passionate vernacular said that we had scored an 'own goal,'" he wrote.
He added: "It's not easy being leader of the opposition. There is always a conga line of trouble waiting at your office door. You're never far away from disagreement.
"And in those tiny moments of rest between the ennui of shadow cabinet meetings, there's a helpful spin doctor who can press a promotional copy of The Sun into your hands."
Margaret Aspinall, chair of the Hillsborough Family Support Group - which represents 75 families - said she could not believe the pictures of the three party leaders and suggested "common sense should have prevailed at a very sensitive time for the families".
And Barry Devonside, of the Hillsborough Justice Campaign, said it is "an absolute disgrace that the leader of the Labour Party got involved".
The Sun backed Labour under Tony Blair but withdrew its support before the 2010 election.
Mr Miliband has had a strained relationship with Rupert Murdoch, the Sun's proprietor, after leading calls for tougher press regulation in the wake of the phone hacking scandal.
Mr Clegg has also been urged to apologise by a Lib Dem councillor in Liverpool for an "error" of judgement in associating himself with the paper's offer.
"I have emailed Nick's advisors to ask what was he doing," Richard Kemp said. "I am particularly surprised at Nick Clegg, as Hillsborough is in his constituency."
He added: "I think he has been badly advised. He is not evil or stupid and I hold his advisers more responsible."
In response, a spokesman for the deputy prime minister said his show of support for the England football team "does not change his views on the Hillsborough tragedy".
"He understands the depth of feeling on Merseyside and elsewhere about what happened and that is why he played a pivotal role in government in ensuring that official documents relating to Hillsborough were released," the spokesman added.
A Conservative source said Mr Miliband's apology was an "extraordinary gaffe" which proved he lacked "moral conviction".