Update 3.30pm: Tony O'Brien says he tried to create an open culture in the HSE where people could tell him when there was problems.
The HSE boss says if he had been made aware of the problems with CervicalCheck or Vicky Phelan's case he could have made the fallout easier for everyone.
He also resisted calls to resign saying he will stay on until the end of his tenure in July.
Mr O'Brien hoped his staff would tell him about serious issues - putting up a sign in his office saying 'speak truth to power'.
He said: "After a round of meetings and briefings on my very first day, it appeared to me that people were reluctant to tell me stuff, so I put the sign up.
"It is not dissimilar to a process that Pat Lam introduced when he was manager of Connacht, the safe zone."
Update 3.25pm: 'I respectfully decline to accept your invitation to resign' - Tony O'Brien
The HSE Director General says he will politely turn down requests for him to step down in the wake of the CervicalCheck scandal.
While the Health Minister has said the crisis has shaken his confidence in the health service.
At the Oireachtas Health Committee this morning Tony O'Brien was asked if he will heed calls to step down.
"I understand your point, I respectfully decline to accept your invitation to resign without prejudice or otherwise," he said.
Minister Simon Harris has said Mr O'Brien should see out his time, despite calls from a number of ministers for him to go.
Mr Harris said: "If your question is in my judgement, is it better that Mr O'Brien serves out his remaining number of weeks and continue to do what we need him to do, to help get the answers, then yes it is, that is my judgement."
But the Minister also said he had concerns about the system Mr O'Brien has presided over.
The HSE boss also batted away questions suggesting he had to have known about the scandal before he says he did.
Mr O'Brien said: "To quote that great philosopher deputy Alan Kelly 'it's so bizzare and unbelievable that it must be true'.
Sinn Féin still plan to bring a motion of no confidence in Tony O'Brien next week.
Update 11.20am: Tony O'Brien 'did not know' about cancer screening scandal
The under-fire head of the Health Service Executive (HSE) has said he did not know about the cervical cancer scandal in time.
Those who should have given him information did not realise the significance of the screening problems, director general Tony O'Brien said.
He called for a duty of candour to be imposed.
"This one I was not and I am very concerned about that."
The Government has ordered a scoping inquiry into the matter.
An audit by CervicalCheck - Ireland's national screening programme - of 1,482 women diagnosed with cervical cancer since 2008 found potential errors in 208 cases as tests showed no abnormality when they should have been given a cancer warning.
Seventeen have since died.
A total of 201 of the women and their families have been offered early meetings, while the remaining seven are abroad and cannot be contacted, health officials said.
Almost 12,000 women have called a helpline.
Tony O’Brien says he is intending to continue in his role as Director General of the HSE pic.twitter.com/GMQbndlyBl— RTÉ News (@rtenews) May 9, 2018
Mr O'Brien told the Joint Health Committee at the Oireachtas: "It would have been beneficial if all the communication had been completed before it came into the public domain. That is what has damaged confidence.
He steps down in July despite calls for him to go sooner, and Sinn Fein leader Mary Lou McDonald has claimed he was "untouchable".
He said he intended to continue work agreed with health minister Simon Harris to meaningfully address all issues of significant concern.
He has a sign in his office, "speak truth to power", put up on his second day after becoming concerned that people were not giving him information.
He said those who should have given him information did not see the significance of it, but supported the introduction of a statutory duty of candour to bring a "sharper edge" to how people acted.
Mr Harris said everyone's confidence had been shaken but Mr O'Brien was best placed to address the issues raised while he served the remainder of his term.
Update 10.50am: HSE boss Tony O'Brien says he will not resign despite pressure from political parties.
Three ministers, Fianna Fáil and Sinn Féin have all shared their belief that Mr O'Brien should step down after the CervicalCheck scandal.
He has told an Oireachtas Committee if he had been made aware of the situation earlier he could have made the fallout easier for everyone.
Watch live here:
When asked by Fianna Fáil's Stephen Donnelly if he would heed the calls to step down, Tony O'Brien said no.
"So while I recognise the concern I believe the effort underway to address that concern is appropriate and meaningful. I understand your point.
Update 10.05am: Simon Harris says his confidence in the Health Service has been shaken by the CervicalCheck scandal.
The Health Minister and the HSE Director General Tony O'Brien are giving a quarterly update to the Oireachtas Health Committee.
Mr O'Brien has told the Oireachtas Health Committee he will not resign.
It has heard Mr O'Brien was meant to be on annual leave this week but cancelled it to deal with CervicalCheck.
Health Minister Simon Harris opened the meeting by addressing the events of the past few weeks.
"This has been an intensely difficult time for everyone involved, most importantly the individuals, the women and their families," he said.
"Fundamental values have been questioned, Honesty, truth, openness; our commitment to these vital principles and values has been questioned."
Update 6.42am: The HSE boss Tony O'Brien is due to appear again before the Health Committee at Leinster House today, as calls continue for his resignation.
He is scheduled to appear alongside the Health Minister Simon Harris to give a quarterly update on the state of the health services.
The hearing is being over-shadowed by the Cervical Check scandal.
Sinn Féin will table a no confidence motion in Mr O'Brien in the Dáil next week.
The party's finance spokesperson Pearse Doherty says someone must be held responsible for the current controversy.
"The HSE completely misinformed the State Claims Agency when they said during the Vicky Phelan case that all women were informed of their misdiagnosis and what we found out two weeks ago is that 162 women were not.
"Do your job, Minister, and tell Mr O'Brien that it's time for him to go."
Fianna Fáil's Health spokesperson Stephen Donnelly also told the Health Minister it is time for Mr O'Brien to step down.
"I would put it to you as well, Minister, that it is an ongoing political error to allow the Director General of the HSE to remain in situ," he said.