The prime minister has "apologised unreservedly" for the "events that took place in Ballymurphy" in 1971, Downing Street has said.
A spokesperson said during a phone call with NI's first and deputy first ministers on Wednesday, Boris Johnson said what happened was "tragic".
An inquest found 10 people who were shot in the wake of an Army operation in Belfast were "entirely innocent".
Families of some of the Ballymurphy victims have rejected the apology.
Politicians in Northern Ireland have also criticised the manner in which it was delivered.
John Teggart, whose father Danny was among those who were killed, said Mr Johnson's comments were an "insult".
"The apology was to third parties, it wasn't to the Ballymurphy families," he said.
"It's not a public apology.
"What kind of insult is it to families that he couldn't have the conversation with ourselves?"
A statement from a Downing Street spokesperson said Mr Johnson told First Minister Arlene Foster and Deputy First Minister Michelle O'Neill he was sorry for the "huge anguish" which had been caused to the families due to their "lengthy pursuit of truth".
The prime minister was "deeply sad" at the findings of the inquest led by Mrs Justice Keegan, it continued.
Among the victims were a priest who was trying to help the wounded and a mother of eight.
Nine of the 10 victims were killed by the Army, the coroner said.
However, she could not definitively rule who shot the tenth victim, John McKerr.
"The prime minister apologised unreservedly on behalf of the UK Government for the events that took place in Ballymurphy and the huge anguish that the lengthy pursuit of truth has caused the families of those killed," Mr Johnson's spokesperson said.
"The prime minister restated the government's intention to deliver a way forward in Northern Ireland that focuses on reconciliation, delivers for victims of the Troubles and ends the cycle of reinvestigations.
"He stressed the importance of working hard to keep the gains made through the Belfast/Good Friday Agreement and of all parties doing their utmost to help the victims' families find out what happened to their loved ones, so that future generations are not burdened by the past."
'Apology means nothing'
Briege Voyle, whose mother Joan Connolly was killed, said the prime minister's apology "means nothing".
"I don't care about an apology, I want to know why [our loved ones were killed]," she told the BBC.
She added it would have been "more respectful" for Mr Johnson to make the apology in parliament, rather than through a phone call.
There are real question marks over the nature of how this apology was issued.
Not by the prime minister at the despatch box in parliament, nor to the families who had been calling for a direct, public apology, but in a readout from Number 10 after a private meeting with Stormont's first and deputy first ministers.
Part of the confusion is that the DUP and Sinn Féin statements giving their version of the call make no reference to any apology from Boris Johnson.
Ultimately, only the politicians who took part in the call and their advisers know exactly what was said, and how it was said.
There is speculation that Brandon Lewis's planned statement to the Commons on Thursday about the inquest's findings will include a public apology.
Given the underwhelming response from the families to the prime minister's words and how this has been handled so far, they may not take much more comfort from what the government says next.
A Sinn Féin spokesperson said the first and deputy first ministers were told that Northern Ireland Secretary Brandon Lewis would make a statement on Ballymurphy on Thursday.
They said: "Michelle O'Neill put it to Boris Johnson that he should apologise to the families of those killed in Ballymurphy by British state forces.
"After 50 years of cover-up and lies they have been vindicated and their innocence declared.
"She challenged attempts by his government to deny the Ballymurphy families, or any other access to justice now or in the future."
Ms O'Neill, Sinn Fein's vice-president, had previously described an apology as the "bare minimum" required by the government.
Taoiseach (Irish Prime Minister) Micheál Martin said: "I would encourage the British government to respond in a comprehensive and fulsome way to the finding that 10 completely innocent people were shot and killed."
He added: "I would encourage them to understand the depth of the pain and grief felt by the families and how that pain and grief was compounded by the untruths that were told about their loved ones.
"This should be done in a manner that respects the wishes of these families."
Alliance Party MP Stephen Farry said it was "helpful" that the government was "prepared to apologise", however, he added a statement needed to be made in parliament on Thursday.
"The scope of apology needs to be scrutinised to ensure it covers all aspects," he continued.
While it is helpful that UKG is prepared to apologise in relation to #Ballymurphy, any apology needs to be made in Parliament tomorrow and crucually directed to the families. The scope of apology needs to be scrutinised to ensure it covers all aspects.https://t.co/3iPDUigj53— Stephen Farry MP (@StephenFarryMP) May 12, 2021
SDLP assembly member Matthew O'Toole tweeted it was "utterly repugnant" for the prime minister to believe it was an "appropriate manner" to issue a statement on the shootings through a spokesperson.