Mr O'Brien told the committee that he rejects Mr Donnelly's call to step down from his position as he would like to continue in his in role in order to address the issues of concern.
Director General of the Health Service Executive (HSE) Tony O'Brien will resign from his position following the CervicalCheck cancer misdiagnosis.
He said, notwithstanding the clear communication failures surrounding the CervicalCheck Audits, he is confident that the Scally Review will demonstrate the quality and value of the CervicalCheck Programme once it is complete.
The HSE statement said "he looks forward to engaging with the Review" and he will provide his full cooperation to the preliminary inquiry headed by Dr Gabriel Scally.
He added that he is proud to have lead the health services and its many staff in "a very challenging environment", and he added that he is "deeply committed to health reform in Ireland".
Varadkar, a doctor and former health minister, said the government shared the anguish of women who were given inaccurate results and announced a support plan for women caught up in the scandal.
The Minister for Health, Simon Harris, thanked Mr O'Brien for his "many years of dedicated public service".
It comes as Global Positioning System admit they're seriously concerned at the undermining of the Cervical Check programme, and that it could result in fewer women getting smear tests.
The IMO says it's agreed a programme for women with concerns to visit their Global Positioning System and if required, organise for a repeat smear test.