Secretary of State Theresa Villiers has rejected calls for an independent review panel to review the 1971 Ballymurphy shootings.
The refusal was made on the grounds a new probe would not be in the public interest.
In a statement, the Ballymurphy families said they were "outraged" at the decision.
The Army's Parachute Regiment was involved in the killings of 11 people, over a three-day period in August 1971.
Ten people died as result of gunfire injuries, among them a Catholic priest and mother of eight, sustained over three days of shooting in August 1971 – an episode relatives refer to as the Ballymurphy massacre – while another man died of a heart attack following an alleged violent confrontation with soldiers.
Theresa Villiers said she did "do not believe that such a review would provide answers which are not already in the public domain or covered by existing legal processes".
"In reaching this decision, I have sought to balance the strong and clear views of the families with the need to ensure that existing legal mechanisms can continue to carry out their functions without being impeded by an additional process. That includes the ongoing Coroner’s inquests."
A new inquest into those deaths caused by gunfire was ordered by Northern Ireland's Attorney General John Larkin in 2011.
The Northern Ireland Office said any additional review would "cut across this ongoing legal process".
The Ballymurphy families have long campaigned for a review panel to be set up by the Government.
They want the probe modelled on the one that re-examined the Hillsborough football stadium disaster.
Theresa Villiers said she was "willing to meet with the Ballymurphy families and their representatives again, if they wish".
At a press conference in west Belfast, Briege Foyle, whose mother Joan Connolly died, ripped up the letter Ms Villiers had sent outlining the decision.
John Teggart, whose father Daniel was one of those killed, said the Government had treated them in a "disrespectful and shameful manner".
"The families have a message for David Cameron," he said.
"When will you stop harbouring the murderers in the ranks of the British army?"