More than 21,000 people have signed an e-petition demanding The Sun reveal its sources for its "The Truth" story in the wake of the Hillsborough tragedy.
Ninety-six Liverpool fans died in the disaster on 15 April 1989.
Four days later, the newspaper claimed Liverpool fans had stolen from the dead and urinated on victims. It later apologised.
The petition calls on The Sun to disclose all sources for the story to the Hillsborough Independent Panel.
If 100,000 people sign the petition, initiated by David Hawkins, the issue could be debated in the House of Commons.
Ninety-five supporters were killed in a crush of fans at Sheffield Wednesday's ground, where the club was playing an FA Cup semi-final against Nottingham Forest. The 96th victim was in a coma for three years and died in 1992.
An independent inquiry led by Lord Chief Justice Taylor in 1989 established that the main cause was a failure of police crowd control.
Margaret Aspinall, who is chair of the Hillsborough Family Support Group and lost her 19-year-old son James in the disaster, said the number of people who had chosen to sign the petition was "humbling".
She said The Sun's coverage had "furthered the injustice" for those who had died, their families and the surviving fans. "They should divulge the name if they have any remorse whatsoever," she added.
"I can't accept an apology but it would be some sort of way of breaking down the barrier," she said.
A previous petition set up by Liverpool fan Brian Irvine, calling for the government to disclose all documents relating to the disaster and its aftermath, attracted 140,000 signatures.
A Commons debate was held on Monday evening, after the backbench business committee agreed it should go ahead.
All papers released
Liverpool Walton MP Steve Rotheram, whose constituency includes Anfield, opened the debate saying there had been a campaign to blame Liverpool fans. He called on the prime minister to issue a formal apology.
He and other MPs also criticised The Sun's story, which prompted thousands of people on Merseyside to boycott the newspaper. Mr Rotheram also attacked a "senior police officer and a Conservative MP" who leaked stories to the press.
Mr Burnham, speaking for the opposition, said the disaster and the events following it, were "one of the biggest injustices of the 20th Century".
Home Secretary Theresa May re-affirmed the government's position that all documents - including cabinet papers - would be released, via the independent panel. Cabinet papers are usually subject to a 30-year rule.
The panel, chaired by the Bishop of Liverpool, James Jones, is expected to report next year.