Culture Secretary Jeremy Hunt has apologised after suggesting that hooliganism played a part in the Hillsborough football disaster.
Ninety-six Liverpool fans were crushed to death on 15 April 1989 at Sheffield Wednesday's Hillsborough stadium.
He praised the England fans at the 2010 World Cup saying the "terrible problems" of "Heysel and Hillsborough in the 1980s seem now to be behind us".
Investigations have found that violence played no part in the tragedy.
Mr Hunt was giving an interview following England's exit from the World Cup, where he applauded the behaviour of fans.
Apologising afterwards, he said: "I know that fan unrest played no part in the terrible events of April 1989 and I apologise to Liverpool fans and the families of those killed and injured in the Hillsborough disaster if my comments caused any offence."
The Prime Minister's official spokesman has said that David Cameron has full confidence in Mr Hunt.
The 96 fans died and hundreds more were injured when a crush developed in the Leppings Lane end of the Hillsborough stadium during an FA Cup semi-final match between Liverpool and Nottingham Forest.
Lord Justice Taylor's official inquiry into the disaster, which reported in 1990, criticised senior police officers on duty at the match for a "failure of control" and recommended the introduction of all-seater stadiums.
Margaret Aspinall, chairman of the Hillsborough Family Support Group, called for a face-to-face meeting with Mr Hunt.
She said: "After all these years of fighting for justice I am very angry that he has shown such ignorance of the facts.
"He is an absolute disgrace."
Mrs Aspinall, who lost her 18-year-old son James in the disaster, said she would not accept Mr Hunt's apology unless she was allowed to meet him and "explain the facts".
She added: "I want him to understand that he has reopened old wounds which should have healed many years ago.
"The problem we have is that Hunt has influence and people listen to him.
"We have fought to move forward but now - thanks to him - it feels like we have taken a step backwards."
Speaking in the House of Commons, Derek Twigg - MP for Halton in Cheshire - said Mr Hunt's remarks were "a disgrace".
He added that he had spoken to relatives of those who had died and they were "deeply distressed".
"How can they have trust in the Government that they will see through the proper release of the Hillsborough files given that that's the view held in high parts of the Government?"
He asked Home Secretary Theresa May to "urgently" meet Mr Hunt and the families of those killed to discuss the matter.
Mrs May said the judicial inquiry into the disaster had been "absolutely clear" that no Liverpool supporters were to blame and she agreed to meet representatives of the families.
The comment has also been criticised by former Culture Secretary Andy Burnham on his Twitter account.
He said it was sad to hear a cabinet minister "echo old slurs" about the disaster.
He called for "more than" an apology and for Mr Hunt to give his "full support" to the new Hillsborough Independent Panel.
"Full truth and nothing less", he added.
Fans heckled the Leigh MP, when he spoke at a memorial service at Anfield on the 20th anniversary of the tragedy.
The Hillsborough Independent Panel is currently overseeing the release of documents not previously made public.
After a two-decade fight, the authorities finally agreed to release more than 30,000 documents of evidence relating to the tragedy.