A scoping inquiry revealed last week that almost 2,400 allegations of historical sexual abuse were recorded by 308 schools run by religious orders.
Speaking on RTÉ’s Morning Ireland on Thursday, Mr Harris said there was a need for an “apology and atonement”.
The Taoiseach added: “I can’t see a scenario where there isn’t a State apology.''
The 700-page report said the claims were made against 884 alleged abusers in day and boarding schools run by 42 religious orders.
The scoping inquiry contacted 73 religious orders that ran or are still running schools, with 42 bearing records of historical sexual abuse allegations.
The fallout of the report saw gardai contacted more than 160 times with allegations – some of which were the first time the individual had come forward.
Mr Harris said: “We have this deep, painful wound now – and I use wound rather than scar because it’s an open wound – it’s hurting today.
“We have people whose pasts were destroyed, and it has resulted in their futures being put on hold.
“And we have seen the most egregious – that’s even too weak a word – breach of trust, responsibility and authority. And it was endemic.”
“And I want to say today as Taoiseach: I am so sorry and I feel such a deep sense of sorrow, hurt, anger and disgust – and we will get this right.”
“ Of course, there's going to be a need for apology and atonement, but there's also a need to get the structure right here. And I'm really trying to dig deep.''
Mr Harris said he would not rule out the compulsory purchase by the State of the assets of religious orders in order to offer compensation to victims.
“I said yesterday and I say today I don't want to use adversarial language. I want people to finally, for once and for all, do the right thing. I want people who, as I say, speak Christianity to practice it, but we can rule nothing out at this stage.”
