Minister for Justice Charlie Flanagan has promised to make the presidents of the Circuit Court and the District Court part of the decision making in judicial appointments.
Mr Flanagan said after all careful consideration the presidents of these courts will be involved in selecting and recommending persons for appointment to their courts.
However, the minister repeated the Government has not moved on its undertaking to have a lay majority and a lay chairperson on the new Judicial Appointments Commission.
Earlier, Taoiseach Leo Varadkar denied that Minister for Transport Shane Ross threatened to resign last Sunday over the Judicial Appointments Commission Bill.
The bill provides for the setting up of a Judicial Appointments Commission made up of a lay majority, including the chairperson.
The change in process to nominate judges was one of the key priorities for Mr Ross and the Independent Alliance during the Programme for Government talks.
Mr Ross secured a commitment from Fine Gael to bring in new legislation in the area.
The Government plans to proceed with the bill as it stands, despite criticism from Fianna Fáil and senior members of the judiciary.
Mr Flanagan also recently wrote to Fine Gael TDs saying he was disappointed by some of Mr Ross’ comments about the judiciary.
However, in a briefing document to his party last night, he stressed the bill was significant and would modernise the process of nominating judges.
It will be debated in the Dáil over the next three days.
During questions to the Taoiseach in the Dáil this afternoon, Sinn Féin deputy leader Mary Lou McDonald asked Mr Varadkar: "Is it true that Shane Ross threatened to pull the plug on your administration?
"Is it true that he threatened to pull the plug on the basis of your handling of the appointment to the Court of Appeal?
"Is it true that he threatened to pull the plug unless you guaranteed him the Judicial Appointment legislation was gotten through the Oireachtas before the house rose for the summer?"
Mr Varadkar said: "I speak to Minister Ross on a regular basis. We did have two phone calls last Sunday. On no occasion in either of those phone calls did he threaten resignation to me.
"I have seen reports that he may have done so in the newspapers but perhaps that was in conversation with other people or other ministers.
"Certainly in neither of the conversations that he had with me did he threaten resignation and I am happy to clarify that."
Ms McDonald asked: "Am I to take from that response that whereas the threat was not made directly to the Taoiseach to bring down the Government, that the threat was made to another minister, another member of Cabinet?"
Mr Varadkar said: "I only know about that from the papers. Certainly no threat was made to me in either telephone conversation on that particular Sunday."
Ms McDonald asked: "Has the Taoiseach ascertained from his cabinet colleagues whether or not there was a threat to bring the government down?"
The Taoiseach said: "If I had to ascertain with Government ministers about every piece of gossip that appears in the newspapers, I would not have time to get any work done."
Fianna Fáil leader Micheál Martin has said there is no rationale for the current proposed bill.
He said that Mr Ross wants to ram this through before the summer recess, to support the Government. He said the motivation behind the legislation is wrong, with the minister portraying the judiciary as self-serving individuals "waiting Buggins' turn".
Mr Martin also said Fianna Fáil believed Chief Justice Susan Denham should be the chairperson of the commission, and this was a kick in the teeth to her. He added that the under-representation of judges was equally unacceptable.
He called on Mr Varadkar to publish a letter written by the presidents of the courts to the Taoiseach, where they expressed their concern on the proposed judicial appointments legislation.
The Taoiseach said he would take advice on whether the letter could be published.
He also said there has been engagement with the judiciary to hear their views on this legislation.
Mr Varadkar said he had immense respect for the Chief Justice who he had known since he was a teenager.
He said the rationale behind the bill was threefold - so the appointments would be less political; more transparent; and not be self appointing or self regulating.
He told the Dáil that having a lay chairperson of the Judicial Appointments Commission is not unusual and it is done this way in Scotland and other countries.
He said this is the "modern way" and it is the method used to appoint senior civil servants, private sector CEOs and hospital consultants.
The Cabinet discussed the bill this morning in what has been described by one source as a "calm discussion" with some "healthy dissent".
The change in process to nominate judges was one of the key priorities for Mr Ross and the Independent Alliance during the Programme for Government talks.
