Ed Miliband has apologised after Labour figures in Liverpool expressed anger at his decision to pose with a copy of The Sun.
The party leader was photographed with a special edition being distributed free to mark the start of the England football team's World Cup campaign.
"Ed Miliband was promoting England's bid to win the World Cup and is proud to do so," a spokesman said.
"But he understands the anger that is felt towards The Sun over Hillsborough by many people and he is sorry to those who feel offended."
The statement came after Liverpool Walton MP Steve Rotheram and city mayor Joe Anderson accused Mr Miliband of failing to take account of continuing fury over the tabloid's coverage of the 1989 disaster, which claimed 96 lives.
Mr Anderson said: "Such clear support for that publication at any time would be wrong but at such a sensitive time is deeply shocking.
"My city was offended and insulted by the lies and smears peddled by The S*n and their hindrance to our fight for justice is something that will never be forgotten.
"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.
"It begs the question - were the comments he made after the Hillsborough panel report sincere or just sound bites?"
Mr Rotheram, who raised concerns with Mr Miliband face-to-face after the picture emerged, posted on Twitter: "He never meant any offence, but in my opinion it shouldn't have happened in the first place."
Margaret Aspinall, chair of the Hillsborough Family Support Group, said Mr Miliband's apology was "a bit late" but criticised all three party leaders.
Mrs Aspinall, attending the inquest into the death of her son James at the Hillsborough inquests in Warrington, added: "Common sense should have prevailed.
"They know the families have got enough to get through right now, they know the feelings of the people, not just in Liverpool, it has spread everywhere.
"I can't understand the insensitivity of what they have done, they didn't show any common sense.
"At this moment in time, it was a stupid thing to do. You have got to think about all the people it affected.
"I have met Mr Cameron, I have met Clegg and I have met Mr Miliband.
"The three of them have been very insensitive here, but more so, I think, Ed Miliband. He should have had more common sense."
All the main party leaders have been pictured with the special edition of the Sun.
Liberal democrat peer Lord Storey, a former mayor and leader of Liverpool City Council, urged Nick Clegg to issue an apology.
"I don't think people outside of Merseyside realise the great upset and harm The Sun caused to the people of this city," he told the BBC's Daily Politics.
"It is an insult to what has happened. Both Miliband and Nick Clegg should clearly apologise for the hurt that they have caused."
Richard Kemp, a Lib Dem councillor in Liverpool, added: "I am particularly surprised at Nick Clegg, as Hillsborough is in his constituency.
"I think he has been badly advised. He is not evil or stupid and I hold his advisers more responsible."
Sun managing editor Stig Abell told BBC radio 4's World at One the special edition was "fun and lighthearted", and stressed it had not been delivered in the Liverpool area.
"We were of course very conscious of the sensitivities around Liverpool," he said.
"The Sun recognises that it was the biggest mistake in the Sun's history.
"It has apologised on numerous occasions for getting something so terribly wrong 25 years ago.
"So we absolutely accept that, we don't expect forgiveness from people in Liverpool and we have been very clear about saying that.
"What we are trying to do.. is celebrating both the idea of a print product getting to 22-odd million houses, and also celebrating the World Cup, Englishness, a feeling that summer is here and people want to have a good time."
Mr Abell added: "Ed Miliband appeared in the back of a black cab talking about the European elections a month ago, he has written for the Sun on Sunday... of course they want to get involved in this because we are trying to do something that unites the nation."
Liverpool West Derby MP Stephen Twigg, a shadow justice minister, said in a statement on his website: "I understand, and share, the anger at The Sun's actions regarding the Hillsborough tragedy and their treatment of the 96 and their families.
"We will not forget the 96 who never came back to Liverpool that day - and will also never forget the reprehensible and wholly false allegations The Sun made at the time.
"Yesterday, I met Ed Miliband to put across the very real anger that people feel. I know he understands and fully appreciates the reasons why Liverpool continues to boycott The Sun. He was not attempting to promote the newspaper, but when asked to pose for a picture to support the England football team at the World Cup, he agreed.
"He regrets any offence that the picture might have caused and he has apologised to those he has offended."
A spokesman for Mr Clegg said: "Nick Clegg offering his 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."