After a lengthy meeting with Stardust representatives in Government Buildings, the Taoiseach said he would also be making an apology in the Dáil on behalf of the State.
In a statement, Mr Harris said the meeting with families and loved ones of the 48 young people who died in the nightclub fire was “humbling and emotional”.
“I want to thank every person who attended for what they told me, both as a group and in private individual conversations,” he said.
“65 people came to the Department of the Taoiseach today. However, I am acutely aware that the numbers affected by Stardust is many, many multiples of that,” he said.
“That includes those injured, the people working in Stardust, the frontline workers who fought to save lives on the night.
“It includes survivors, the fire crews, the ambulance staff, the gardaí, the army, the taxi drivers and the communities across Ireland who have carried this tragedy with them for 43 years.
“I have listened closely to everything the families told me and as Taoiseach, I have today apologised unreservedly to each family. I will do so on behalf of the state on Tuesday next,” he added.
On Thursday, an inquest jury returned a verdict that they were all unlawfully killed.
It comes after a previous finding in 1982 that the fire had been started deliberately.
A majority decision from the jury of seven women and five men found the blaze, which broke out in the early hours of Valentine’s Day 1981, was caused by an electrical fault in the hot press of the bar.
Susan Behan, whose brother John Colgan was among those killed, said the Government should issue an official state apology, describing it as “the right thing to do”.
The Taoiseach said on Friday: “I am very keen to meet with the families and very conscious that these families have felt unheard for decades, and I want to make sure that they know that I’m listening, that I want to hear them and, of course, I want to be in a position as Taoiseach to apologise on behalf of this country, but I think the most appropriate thing to do is to meet with them.”
He added: “I am eager to be in a position to apologise to these families but I think it’s right and proper that I meet them first.”
On Saturday, the families walked with a banner remembering their relatives towards Government Buildings.
They were greeted by the Taoiseach who spoke to them in the courtyard and shook their hands before going into the official meeting.
Prior to their engagement with Mr Harris, the families also met Sinn Fein leader Mary Lou McDonald.
She said a full state apology to the Stardust families is “essential”.
Ms McDonald said: “For four decades, they have faced obstacle after obstacle put in front of them by the State.
“That is why it is vital that a State apology is now made and that it address the failures of governments not just 43 years ago in the aftermath of this tragedy but every day since then.
“They had to fight until 2019 to get a second inquest and they had to continue to fight the State every day until the inquest started.
“They had to fight to ensure that the resources were in place so every family could participate in the inquest and get access to justice.
“They have to fight for jurors to have their income protected and to be selected in a transparent way as they would in the court system.
“Coroner Dr Myra Cullinane at the start of the Inquest said the 48 victims who died in the fire would be central to proceedings and she honoured that commitment.
“It is vital that the State now does the same today.”