Police and emergency services made "strenuous attempts" to deflect the blame for the Hillsborough disaster onto innocent fans, documents about the tragedy revealed.
The disclosures were made by the Hillsborough Independent Panel, which has been overseeing the release of thousands of official documents relating to Britain's deadliest sporting disaster.
Mr Cameron said that Attorney General Dominic Grieve will review the report as quickly as possible in order to decide whether to apply to the High Court to quash the original, flawed inquest and order a new one. It will be for the court to make the final decision.
Wednesday's report showed that the Hillsborough families had suffered a "double injustice", both in the "failure of the state to protect their loved ones and the indefensible wait to get to the truth", and in the efforts to denigrate the deceased and suggest that they were "somehow at fault for their own deaths," said Mr Cameron.
He told MPs: "With the weight of the new evidence in this report, it is right for me today [Wednesday] as Prime Minister to make a proper apology to the families of the 96 for all they have suffered over the past 23 years.
"On behalf of the Government - and indeed our country - I am profoundly sorry for this double injustice that has been left uncorrected for so long."
Ninety six Liverpool supporters died in a crush at Sheffield Wednesday's Hillsborough stadium on April 15, 1989 where their team were to meet Nottingham Forest in an FA Cup semi-final.
Introducing the report to the Hillsborough families at the Anglican Cathedral in Liverpool, Bishop James Jones, the Bishop of Liverpool and chairman of the panel, said: "For nearly a quarter of a century the families of the 96 and the survivors of Hillsborough have nursed an open wound waiting for answers to unresolved questions. It has been a frustrating and painful experience adding to their grief.
"In spite of all the investigations they have sensed that their search for truth and justice has been thwarted and that no-one has been held accountable.
"The documents disclosed to and analysed by the panel show that the tragedy should never have happened. There were clear operational failures in response to the disaster and in its aftermath there were strenuous attempts to deflect the blame onto the fans. The panel's detailed report shows how vulnerable victims, survivors and their families are when transparency and accountability are compromised.
"My colleagues and I were from the start of our work impressed by the dignified determination of the families."
In its summary the panel said: "It is evident from analysis of the various investigations that from the outset South Yorkshire Police sought to deflect responsibility for the disaster on to Liverpool fans ... there is no evidence to support this view."
They went on to say the wrongful allegations about the fans' behaviour later printed in some newspapers, particularly The Sun, originated from "a Sheffield press agency, senior SYP officers, an SYP Police Federation spokesperson and a local MP".
The panel said the Police Federation, "supported informally by the SYP Chief Constable", sought to develop and publicise a version of events derived in police officers' allegations of drunkenness, ticketless fans and violence.
"The vast majority of fans on the pitch assisted in rescuing and evaluating the injured and the dead," the panel said.
The panel also found that access to Cabinet documents revealed that in an exchange about her Government welcoming the Taylor Report into the tragedy Prime Minister Margaret Thatcher expressed her concern that the "broad thrust" of the report constituted a "devastating criticism of the police".
The Prime Minister said: "What happened that day - and since - was wrong.
"It was wrong that the responsible authorities knew Hillsborough did not meet minimum safety standards and yet still allowed the match to go ahead.
"It was wrong that the families have had to wait for so long - and fight so hard - just to get to the truth.
"And it was wrong that the police changed the records of what happened and tried to blame the fans.
"We ask the police to do difficult and often very dangerous things on our behalf, and South Yorkshire Police is a very different organisation today from what it was then.
"But we do the many, many honourable police men and women a great disservice if we try to defend the indefensible.
"It was also wrong that neither Lord Justice Taylor nor the Coroner looked properly at the response of the other emergency services."
The report also says "there was no evidence to support the proposition that alcohol played any part in the genesis of the disaster and it is regrettable that those in positions of responsibility created and promoted a portrayal of drunkenness as contributing to the occurrence of the disaster and the ensuing loss of life without substantiating the evidence".
Mr Cameron said that the Hillsborough disaster was "one of the greatest peacetime tragedies of the last century".