Boris Johnson is facing anger from the families of the 10 innocent civilians killed in Ballymurphy in 1971 over his failure to offer a more formal apology.
The prime minister has been accused of "bad manners" and of neglecting to be "serious" in his response to the verdict of fresh inquests into the shootings in west Belfast.
On Tuesday, a coroner concluded the victims of shootings over three days in August 1971 were "entirely innocent" and the British Army was responsible for nine of the fatal shootings.
Mrs Justice Keegan found that the use of lethal force by soldiers was not justified.
She also criticised the lack of investigation into the 10th death, that of John McKerr, and said she could not definitively rule who had shot him.
Mr Johnson held a call with Northern Ireland’s First Minister Arlene Foster and deputy first minister Michelle O’Neill on Wednesday.
A Downing Street spokesperson said the prime minister had described the conclusions of the Ballymurphy Inquest into the "tragic" events as "deeply sad".
"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," the spokesperson added.
"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."
However, the families of those who were killed almost 50 years ago have criticised the way Mr Johnson’s apology was delivered.
John Teggart, whose father Daniel was among those shot dead at Ballymurphy, told Sky News he had received no approach from the prime minister’s office.
"There was an apology done but in a way, it’s bad manners," he said. "He didn’t approach the families. He didn’t let the families know what was happening.
"A journalist had phoned me when I was sitting in my home today and that’s how I found out."
He added: "Boris Johnson leaks what was said in three-way conversation, a private conversation by the way, to the media. That’s how the families found out.
"I would say to Boris Johnson when it comes to your apology, it needs to be serious.
"You have to apologise for the wrong that was done. You have to apologise and accept responsibility for what was done.
"If he’s coming any way half-heartedly to apologise like that, he knows what he can do with it."
Mr Teggart said former prime minister David Cameron had "set a precedent of the way things should be done" with his response in 2010 to the findings of an inquiry into the Bloody Sunday killings in 1972.
Mr Cameron used a House of Commons statement to apologise to the families of those killed.
"His office had contacted the Bloody Sunday families so the Bloody Sunday families knew exactly what was coming," Mr Teggart added.
Briege Voyle, whose mother Joan Connolly was killed in Ballymurphy, also dismissed Mr Johnson’s apology.
"His apology means nothing, we need him to go back to the Ministry of Defence and tell them to tell the truth, tell our legal team the names of the soldiers who murdered our loved ones and ask them why," she said.
She added an apology by Mr Johnson in the Commons would have "at least been a bit more respectful… as if he is holding us in a wee bit of respect but to do it this way is trying to push it under the carpet".
Meanwhile, Mrs Foster made no reference to Mr Johnson’s apology in her own comments following their remote meeting.
And Ms O’Neill, after speaking with the prime minister, revealed she had "put to him 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 & their innocence declared," she added on Twitter.
"Attempts to deny access to justice reprehensible."
Northern Ireland Secretary Brandon Lewis is due to make a statement on the findings of the Ballymurphy inquest to the House of Commons on Thursday.
Analysis: To understand families’ anger you need to rewind 10 years
By David Blevins, senior Ireland correspondent
To understand why the Ballymurphy families are so offended by the prime minister’s apology you need to rewind 10 years.
In June 2011, victims of the Bloody Sunday shootings in Londonderry were declared innocent by a public inquiry.
Within minutes, the then prime minister David Cameron stood in the House of Commons and publicly apologised to the families in Derry.
On Tuesday, when a coroner found the victims of the Ballymurphy shootings innocent, the government was announcing plans to halt historical prosecutions in Northern Ireland.
And 24 hours later, the families of the nine men and one woman who died when British troops opened fire in west Belfast in 1971 had received no public apology.
What they did finally receive was a second-hand apology – allegedly given to Northern Ireland’s first and deputy first ministers in a virtual meeting.
A spokesperson for the prime minister said Boris Johnson had "apologised unreservedly on behalf of the UK government".
But read-outs of the call from the first and deputy first minister made no reference to any such apology having been given.
It is now blindingly obvious that a statement to the Commons by Northern Ireland Secretary Brandon Lewis on Thursday will not be enough.