A campaign has begun after the Cabinet Office said it was to appeal a ruling by the information commissioner which demanded the papers be made available.
Dalglish, who was the manager of Liverpool on the day of the disaster in 1989 and subsequently attended the funerals of many of the dead, used his official Twitter account to urge people to sign an e-petition calling for full disclosure.
Can't keep it quiet: Liverpool manager Kenny Dalglish has called on supporters to back a petition demanding the release of Hillsborough files
He wrote: 'Please sign this petition and RT. Think it is very important that we support this.'
The petition, which is a registered on the government's website and has already been signed by 21,000 people, calls for 'full government disclosure and publication of all documents, discussions and reports relating to the 1989 Hillsborough disaster'.
Several members of parliament are also behind the push to see the files made available, with Labour MP for Leigh and former Culture Secretary Andy Burnham particularly vocal in his displeasure at the recent appeal against their release.
Tragedy: 96 people died as a result of the Hillsborough stadium disaster in 1989
Mr Burnham, an Everton fan, took to Twitter, and said: 'Families must have the full truth. Nothing less will do. I will write to Prime Minister urging him to intervene & drop this appeal.' He signed off with '#jft96', which means 'Justice For The 96', a campaign in honour of those who died.
Steve Rotheram MP added: 'Andy Burnham MP, Merseyside MPs and I are to ask Cameron to intervene to get Hillsborough Cabinet minutes released. Transparent Government!!'
The judgement by the information commissioner related to a Freedom of Information request from the BBC which was refused by the Cabinet Office in 2009. The Cabinet Office said releasing the documents would interfere with the inquiry by the Hillsborough Independent Panel.
Close to home: Dalglish went to great lengths to attend as many funerals as he could
The withheld files include reports seen by then-Prime Minister Margaret Thatcher, correspondence between her office and the then-Home Secretary Douglas Hurd and minutes of meetings she attended.
Ninety-five supporters were killed in a crush of fans at the stadium in Sheffield during an FA Cup semi-final against Nottingham Forest in 1989, while another died three years later having been left in a coma.
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