British Prime Minister Boris Johnson is to write to the families of the Ballymurphy victims in person to apologise for their deaths.
Northern Ireland Secretary Brandon Lewis told the House of Commons Mr Johnson would contact the families as he said the Government is "truly sorry" for the events 50 years ago which left 10 innocent people dead.
Mr Johnson yesterday apologised to Northern Ireland's First and Deputy First Ministers, but faced criticism from the families of the victims.
Mr Lewis said: "The events of Ballymurphy should never have happened, the families of those who were killed should never have had to experience the grief and trauma of that loss.
"They should have not had to wait nearly five decades for the judgment this week, nor have been compelled to relive that terrible time in August 1971 again and again in their long, distressing quest for truth."
He went on: "The vast majority of those who served in Northern Ireland did so with great dignity and professionalism, but it is clear that in some cases, the security forces and the Army made terrible errors too."
Mr Lewis added: "There is no doubt that what happened on those awful few days in Ballymurphy also fuelled further violence and escalation, particularly in the early years of the Troubles.
"The Government profoundly regrets and is truly sorry for these events, and how investigations after these terrible events were handled, and the additional pain that the families have had to endure in their fight to clear the names of their loved ones since they began their campaign almost five decades ago."
Brandon Lewis said "thousands of murders remain unresolved" in Northern Ireland, with many families yearning for answers.
He told MPs: "With each passing year the integrity of evidence and the prospect of prosecution do diminish, and the Government is not shrinking away from those challenges.
"We are determined to address them in a way that reflects the time that has passed, the complexity of Northern Ireland's troubled history and the reality of compromises that have already been made.
"But above all we're determined to address it in a way that enables victims and survivors to get to the truth which they deserve. We must never ignore or dismiss the past, learning what we can we must find a way to move beyond it - and the coroner's findings this week are part of that very often painful process.
"This Government wants to deliver a way forward in addressing the legacy of the past in Northern Ireland, one that will allow all individuals of families who want information to seek and receive answers about what happened during the Troubles with far less delay and distress.
"We want a path forward which will also pave the way for wider societal reconciliation for all communities, allowing all the people of Northern Ireland to focus on building a shared, stable, peaceful and prosperous future."