The Opposition is considering "all options" as they claim Justice Minister Helen McEntee is setting "a dangerous precedent" by not appearing before the Dáil for questions from them on Séamus Woulfe.
Opposition parties want Ms McEntee to make herself available for questioning on how Mr Woulfe, the former Attorney General and long-time Fine Gael member, came to be appointed a Supreme Court justice.
The Government has offered to bring forward priority and oral questions for Minister McEntee. However, the offer was rescinded last Friday when the Opposition rejected the proposal as the questions are pre-submitted.
Helen McEntee said: "There is no issue with me answering questions and I'm very happy to do so. I offered to change priority questions at a time of suiting. Every party said no. The suggestion is that priority questions don't hold Ministers to account. I would say that every week ministers answer priority questions from deputies, it has existed for many years."
Micheál Martin, however, denied there was any "political horse-trading" involved in Mr Woulfe's appointment.
"As far as I'm concerned, JAAB, which is chaired by the Chief Justice, has the Presidents of the Four Courts and members of the Law Society. I did not ignore their recommendation. I did not want to embroil myself in the politics of this."
All opposition parties are united that the minister must appear before the Dáil.
Sinn Féin's Padraig MacLochlainn said: "Yesterday, all seven opposition parties and groups requested that an urgent meeting of the Dáil business committee be convened to address the ongoing failure of Helen McEntee to come before the Dáil and take statements and questions.
"The Government's position is, they're not even open to negotiate on this, they're not going to talk about it.
"I don't recall all seven opposition groups and parties coming together on an issue as decisively as this."
The Social Democrats have also requested that the Taoiseach "end the charade" and ensure Ms McEntee appears and takes questions over a "reasonable period", while Labour says the issue is "not going away".
Taoiseach playing into false narrative that his Fine Gael colleagues have been peddling for past few weeks, @RoisinShortall tells the #Dáil. Needs to insist that Minister for Justice comes into House and answers questions on Supreme Court appointment. Accountability at stake. pic.twitter.com/GqAlAhfM6X— Social Democrats (@SocDems) November 24, 2020
"She's still refusing, quite frankly, as a minister who actually under the Constitution has no choice but to go in front of the Dáil," Alan Kelly said.
"This government is running scared. That raises its own questions. This will not go away."