Labour Leader Ed Miliband said he wanted to reaffirm the previous Government's apology over what happened Stafford Hospital. He added: "We on this side are truly sorry."
The Prime Minister said the "shocking truth is this precious principal of British life was broken in Mid Staffordshire".
David Cameron said a new post for the Chief Inspector of Hospitals would be created from the autumn.
The Prime Minister said there will be a new "single failure regime where the suspension of the board can be triggered by failures in care as well as failures in finance".
David Cameron apologised for the way the system had allowed "horrific abuse to go unchecked and unchallenged" for so long.
Speaking on behalf of the Government and the country he said: 'I'm truly sorry'.
David Cameron said the report's evidence of systemic failure means "we cannot say with confidence that failings of care are limited to one hospital".
– Prime Minister
What happened at the Mid Staffordshire NHS Foundation Trust between 2005 and 2009 was not just wrong, it was truly dreadful.
In the scathing report Robert Francis QC attacked local health authorities and the trust board but he refused to blame any individual for failures at the trust.
However, the families of victims are calling for "accountability" and for the NHS Commissioning Board chief executive Sir David Nicholson to resign over the scandal.
Speaking as the report was published, inquiry chair Robert Francis QC said it was a "story of appalling and unnecessary suffering of hundreds of people."