Speaking after Prime Minister's Questions he said many of the findings "are deeply distressing".
New evidence - released today by Hillsborough Independent Panel - showed that police "tried to change the record of evidence".
In all, said Mr Cameron, 164 police statements were altered - including the removal of 116 negative comments about the leadership of the police, to push the blame for the tragedy onto the fans.
In his most damning remark he confirmed that police "tried to change the evidence and blame the fans".
Issuing his apology, the Prime Minister said: "On behalf of the country I am profoundly sorry for the double injustice suffered by the familes of the victims.
The new evidence raised "must be examined", and the Attorney General would be considering it as quickly as possible.
The Prime Minister said the panel had found the safety of the crowds at Hillsborough had been "compromised at every level".
Downing Street confirmed that Mr Cameron received a copy of the Hillsborough report this morning, after it was seen by the families.
The Prime Minister said there was no evidence of government departments trying to conceal the truth.
The Hillsborough Independent Panel this morning released 400,000 pages of previously unpublished official documents relating to the disaster
The families of the 96 football fans who died in Britain's deadliest sporting disaster were the first to see documents from 8am.
A report into the disaster by Lord Justice Taylor, published in 1990, found that the main reason for the disaster was a failure of "police control" but the Crown Prosecution Service decided there was insufficient evidence to bring a prosecution.
The victims' families say it is an injustice that no individual or organisation has been held fully accountable for the disaster. They believe a major incident plan was never initiated by South Yorkshire Police and fans in the Leppings Lane end were denied emergency medical attention.
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