Ms Ní Raghallaigh released a statement saying that it had become "abundantly clear" that she had lost the confidence of Media Minister Catherine Martin, who had alleged that she had been "misinformed" by her twice this week, regarding the Board approval of recent exit packages.
The minister said that she had been left "deeply disappointed", and had requested to meet Ms Ní Raghallaigh in person to discuss this issue.
"It is abundantly clear from statements today, and in particular last night's Prime Time broadcast, that I no longer have the confidence of the Minister in my role as Chair of the Board of RTÉ and that, as such, my position is no longer tenable", Ms Ní Raghallaigh said.
"This evening, after consultation with the Board and Director General Kevin Bakhurst, I have decided to resign from my position".
Elsewhere, Ms Ní Raghallaigh insisted that she did not make an "intentional misrepresentation" to Ms Martin.
"Under the new terms of reference of the Remuneration Committee of the RTÉ Board, all changes to executive pay and terms must be approved by committee", she continued. "This was introduced as part of a wide range of measures to strengthen controls and fully restore public trust in corporate governance at RTÉ".
"Kevin Bakhurst brought the exit of Rory Coveney from RTÉ (announced on Sunday 9th July) to my attention, while the exit of Richard Collins was brought to and approved by the Remuneration Committee of the Board of RTÉ on October 9th 2023".
"I informed the Department about the process which led to Richard’s departure from RTÉ, on October 10th, the day after it was approved at the Remuneration Committee".
"I met with the Minister and her officials, with the Director General, on two occasions for more than three hours this week, dealing with multiple questions across a wide range of issues.
"I was asked if the Board knew about the exit packages for Rory Coveney and Richard Collins. I said that I was aware of them, but they had not come before the full Board", she added. "However, I neglected to recollect that Richard Collin’s exit package did go before the Renumeration Committee."
"This was not an intentional misrepresentation, and I subsequently contacted the Department to clarify the details and remind them that I had previously appraised them of the matter in October".
Ms Ní Raghallaigh's concluded her statement by saying, "Serving as Chair of the RTÉ Board is a privilege which requires the confidence of the Minister. It is abundantly clear that I no longer do".
"My resignation is a source of sadness to me, but it is unavoidable".
"There is a very urgent need for the funding model of RTÉ to be restored and for the transformation process to continue apace. I do not want this matter to distract from that. That must remain our unswerving collective objective".
In a statement Director-General Kevin Bakhurst said that Ms Ní Raghallaigh was an "excellent Chair", who would be "sorely missed", praising her for "her integrity, hard work, commitment to public service".
Mr Bakhurst also called Siún Ní Raghallaigh a "great support to me throughout an incredibly challenging time for RTÉ".
He also added, "Without Siún's experience, insight, guidance and optimism, beginning the process of meaningfully transforming RTÉ would have been a bigger challenge".
