The Taoiseach has said that all matters at RTÉ need to be examined with possible "remedial steps" to restore "trust and confidence".
In a statement, Leo Varadkar said that he was very concerned at the information set out in RTÉ's statement and the suspension of Dee Forbes as Director General.
He said that Minister for Media Catherine Martin is meeting RTÉ's chairperson Siún Ní Raghallaigh tomorrow, where details on the issues involved and the steps the RTÉ Board is taking will be sought.
Mr Varadkar said: "The Government considers it essential that we have the highest standards of governance, accountability and transparency from RTÉ and will consider what further action may be required.
"All of the matters involved will have to be examined and, perhaps, remedial steps taken to restore trust and confidence.
"It will be equally important for the Board to demonstrate that it is putting in place appropriate structures and processes to prevent a recurrence."
Minister Martin is meeting Ms Ní Raghallaigh following revelations that the station paid Ryan Tubridy hundreds of thousands of euro more over a period of several years than it declared to the public and the Oireachtas.
The meeting had been originally scheduled for Monday.
Ms Martin said she was made aware yesterday of the suspension of Ms Forbes, but said she was told the RTÉ Board had to take legal advice before that information could be divulged to the public.
This morning, the RTÉ Board confirmed that Ms Forbes was suspended from her employment on Wednesday.
"I think for the sake of transparency, it is good that announcement has been made," Minister Martin said.
The board had acted swiftly and were doing what needed to be done, she said.
Speaking in Dublin, Minister Martin said she has significant concerns after reading the details of RTÉ's statement yesterday and had already had a follow-up phone call with Ms Ní Raghallaigh.
"I want to know what actions are going to be taken, what process will be put in place to make sure it never happens again and I do believe it raises concerns in relation to the broader transparency and governance of this organisation," Ms Martin said.
Asked whether Mr Tubridy should resign and whether he had further questions to answer in relation to his statement yesterday, Ms Martin said she would not make comments on what individuals or organisations needed to do.
She said that was beyond her remit under legislation.
In a statement this evening, Ryan Tubridy apologised "unreservedly" and said he takes responsibility for failing to ask questions over why RTÉ published incorrect figures about his earnings.
Ms Martin denied that she knew the nature of this issue since March, but said she was told then that an issue had arisen during a routine annual audit and that a fact-finding review was needed to establish the actual facts.
She said there was a question there about the future funding model of RTÉ which was something her department had been examining, and this had to be done in an environment of trust with the public.
Asked if Ms Forbes had managed to leave the organisation without fully answering questions, Minister Martin said due process must be followed on this and said she did not want to comment further on that.
'Comprehensive clarity' needed, says Tánaiste
Earlier, the Tánaiste said there is "huge shock and surprise" at the revelations about payments to Mr Tubridy.
Micheál Martin said: "I think we need more clarification... and I do think we need comprehensive clarity around this, and an explanation as to what transpired.
"I think, particularly in the area of transparency, this is a breach of trust in terms of the public presentation of the figures as opposed to the reality of the figures.
"That is serious, particularly because I think it relates to governance within RTÉ and given its unique role as a public service broadcaster clarity is required in all aspects of this - the role of commercial sponsors in such a flagship programme, (it is) understandable sponsorship is there, but nonetheless there are questions."
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Sinn Féin TD and Chair of the Dáil Public Accounts Committee Brian Stanley said he was demanding immediate explanations and accountability from RTÉ.
Speaking on RTÉ's Morning Ireland, he said he is personally very disappointed as senior people from RTÉ, including Ms Forbes, have been before the committee a number of times over the past few years and gave firm commitments that pay across the top ten presenters was being reduced.
"Not alone did that not happen in this case, in actual fact there were €75,000s being added on, there were €50,000s being added on ... This is at a time when RTÉ was coming into us, RTÉ senior management pleading that the finances of the organisation were in such bad shape. And that is the context here," he said.
Mr Stanley said he did not know why the matter took so long to come out in an internal audit, that it had been going on for five years and there are huge questions around governance and accountability.
Labour TD Alan Kelly, who is a member of the PAC, has said that the committee wants to hear from a number of RTÉ's current and previous management, including Ms Forbes.
"We sent out an invitation and we expect them to honour it. I think it wouldn't be plausible or acceptable to the public now if they didn’t honour it," Mr Kelly said on RTÉ's Six One News.
"We want to hear from the Executive. We want to hear from the Chairperson. We want to hear from the previous chairperson, and we also want to hear from Dee Forbes and all of the executives who are in charge of remuneration and payments across RTÉ," he added.
The Joint Oireachtas Committee on Tourism, Culture, Arts, Sport and Media has called on the Director General and Executive Board to RTÉ to "publicly outline the extent and severity of the issues involved, and the remedial actions that it has taken and that it will take in order to restore and ensure transparency and accountability to those it serves".
It said it plans to formally invite relevant personnel in RTÉ to appear before it next week in public session to give discuss relevant matters.
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RTÉ's full statement on payments to Ryan Tubridy
RTÉ has apologised for what it described as a breach of trust.
The payments were uncovered after the company's auditors alerted the board to some of the transactions.
The statement said that a review found that under a separate agreement Mr Tubridy was guaranteed by RTÉ an additional annual income of €75,000, which was intended to come from a commercial partner.
The payment in 2020 did come from a commercial partner of the station, in exchange for a number of personal appearances a year.
"As part of this agreement, RTÉ in turn issued a credit note to the commercial partner thereby reducing the cost to it of its overall sponsorship arrangement with the organisation," RTÉ said.
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"The commercial partner did not renew this agreement for a second year, and since the agreement was guaranteed and underwritten by RTÉ, the payments were instead made directly by RTÉ to Mr Tubridy's agent (on his behalf)."
As a result, Mr Tubridy received two payments of €75,000, totalling €150,000, in 2022 for that year and the previous year. €18,750 of that related to earnings for the first three months of 2023.
Additional reporting Paul Cunningham, Brian O'Donovan, Joan O'Sullivan and Sinéad Hussey