Sinn Féin leader Mary Lou McDonald has said Brian Stanley has written to the Ceann Comhairle to request time to make a statement to the Dáil on 15 December.
Ms McDonald, who met with the Laois-Offaly TD today, said she told him to "take next week to be with his family; for whom this period of public controversy and comment has proven very difficult".
She said they had "discussed the ongoing public commentary relating to tweets he has posted and a radio interview he gave in March".
The Taoiseach has said the credibility of the Dáil's Public Accounts Committee has been called into question by the controversy surrounding the tweets of its chairman.
Micheál Martin said this is something that Brian Stanley "has to reflect on".
He said he is not entirely satisfied with the apology given by Mr Stanley, which he said was not "comprehensive enough".
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Read more: Stanley faces renewed pressure following criticism of 2017 tweet
Taoiseach Micheál Martin has said the credibility of the Dáil's Public Accounts Committee has been called into question by the controversy surrounding the tweets of its chairman, Brian Stanley | Read more: https://t.co/tVgquDLRKl pic.twitter.com/VTLCikwidv
— RTÉ News (@rtenews) December 4, 2020
Earlier, Minister for Finance Paschal Donohoe said the Sinn Féin TD had questions to answer on whether he should remain in his role as chairperson of the Public Accounts Committee.
Speaking on RTÉ's Morning Ireland, Mr Donohoe said Mr Stanley's apology following the controversy around his recent online comments was "not enough".
He said what Mr Stanley had said, as well as his tweet referencing Leo Varadkar from 2017, was "utterly unacceptable".
The tweet sent by Mr Stanley following Mr Varadkar's election as leader of Fine Gael read "Yippee 4 d tory. it's Leo. U can do what u like in bed but don't look 4 a pay rise the next morning".
Mr Stanley said that the word "yippee" was a celebration of gay rights, given that Ireland had a gay taoiseach.
Mr Donohoe said Mr Stanley "could not be making those comments in that kind of tone about anybody".
"You cannot link up somebody's sexuality with the job that they do. We're a different and better country than that", Mr Donohoe he said.
"It is reflective of the general tone that Sinn Féin take about politics and they take about politicians that they oppose," he added.
Speaking on a Brian Stanley tweet, Minister for Finance Paschal Donohoe says: "You cannot link up somebody's sexuality with the job that they do. We're a different and better country than that." pic.twitter.com/5fRQ6d7tm1
— RTÉ News (@rtenews) December 4, 2020
He said if Mr Stanley could not provide "a credible explanation or answer the question regarding why he believes a tweet like that is unacceptable", then he "has questions to answer regarding why he should stay" in his role as PAC chair.
Mr Donohoe said the bigger question now was why did Mr Stanley delete his Twitter account.
The minister questioned what other comments may have been there and said Mr Stanley now needed to answer the question as to why he should stay in his role as PAC chairperson.
Mr Donohoe earlier said Mary Lou McDonald needs to answer those questions today.
He said: "They are questions that Mary Lou McDonald and that Sinn Féin must answer today.
"Their tone on politics, their tone about how they speak about those who have different political views to them, at many times and in many cases, I don't believe it's acceptable.
"And I believe it poisons the well of how we debate politics in our country."
Meanwhile, Sinn Féin's Louise O'Reilly has said that the tone of the tweet in 2017 referencing Leo Varadkar by her party colleague "was not acceptable".
Speaking to RTÉ News, she said that "if any offence was caused, of course Brian needs to engage and he needs to have those discussions with people".
Ms O'Reilly said that "as a party colleague" she knew Mr Stanley to be an "ally to the LGBT community" and a "very, very staunch campaigner, not just for LGBT rights but also for human rights".
Ms O'Reilly said that it was important to understand the tweet in context.
"At the time in 2017, not just here in Ireland, but the whole world was talking about the fact that we had elected an openly gay head of government.
"It is something for which we should rightly be proud, and Brian Stanley's remarks are in that context."
However, Ms O'Reilly said that "clearly the tweet was left open to misinterpretation".
Ms O'Reilly said that "Twitter is not the platform for everybody, not everybody is suited to engagement on Twitter".
When asked if it was a platform for Mr Stanley, Ms O'Reilly responded by saying "Brian Stanley is not on Twitter anymore, and as I've said it's not for everybody".