Lord Saville’s 12-year inquiry concluded that the British fired the first shots and that they were not reacting to a real or perceived threat, Cameron told the British parliament on the official presentation of the 5,000-page report.
The report says that some of the victims were clearly running away from the shooting.
The shootings were “unjustified and unjustifiable”, he said, but he also pointed out that the report concludes that Martin McGuinness, now a leader of the nationalist Sinn Fein party and deputy First Minister of Northern Ireland, was present and probably armed.
McGuinness, who was in command of the Catholic-based Irish Republican Army in Derry at the time, insisted that the report will not open up new divisions, ahead of its publication.
The mainly Protestant Democratic Unionist Party (DUP), whose leader Peter Robinson is Northern Ireland's first minister, has criticised the inquiry, saying it has created a "hierarchy of victims" in Northern Ireland.
A crowd of thousands, including relatives of the victims, greeted the publication with cheers.
Speakers there demanded that soldiers involved in the shooting should be stripped of their medals.
Neither the prime minister nor the report can decide whether prosecutions should go ahead, although the prosecution service could do so and private prosecutions might also be pressed.