The Bar Council of Ireland has called for private talks to begin between judges and the Government in the row over judicial independence.
The council, which represents barristers, said judges had raised legitimate concerns that should be addressed.
The Law Society has expressed dismay at tensions between the Government and the judiciary.
It said this strain has the potential to cause major damage to the democratic system in Ireland and to the country's reputation abroad.
Earlier, the Master of the High Court Edmund Honohan was criticised for his contribution to the debate, in which he said concerns about judicial independence were over the top.
The President of the High Court, Mr Justice Nicholas Kearns, said Master Honohan had no authority to speak on behalf of the court or its judges.
Mr Honohan had said he felt the row between the Government and the judiciary erupted out of a "sense of entitlement" that judges should be consulted over any proposed new legislation.
The High Court Master said it was inappropriate for anyone, even a High Court judge, to suggest that there might be a question mark against the administration of justice.
In a statement this morning, Mr Justice Kearns said concerns about judicial independence expressed by the Association of Judges were well founded.
He said he hoped every effort would be made to address them.
Mr Justice Kearns, who is not a member of the association, described the present situation as "highly undesirable".
He said he wished to clarify that the Master of the High Court was not a judge but an office holder with what he described as "limited functions" created by statute.
The Association of Judges said the Master of the High Court is a quasi-judicial officer only and is not, and has never been, privy to, or a participant in, dealings of any sort between the judiciary and the executive.
Judges claim independence threatened
The AJI yesterday threw its support behind High Court judge Mr Justice Peter Kelly, who had originally accused the Government of demolishing the judicial system.
Judges are angry over a range of issues, which they say threaten their independence, including pay, pensions and future appointments.
Mr Honohan said there was no question that the judicial independence and integrity was under challenge in any way.
He said: "I'm sorry to say this, but I think Judge Kelly has got it wrong. He's over the top here.
"Judges, when they're appointed, leave politics behind them.
"Now all of this brouhaha seems to be about some sort of sense of entitlement that judges are entitled to be consulted when the minister or the Government proposes new legislation of one sort or another. Sorry, but that's just not correct."
Mr Honohan said the Minister for Justice was not obliged to consult with judges and that, in this instance, Alan Shatter had a better grasp of constitutional propriety.
He said: "Really there is no need for this hysteria about it and it seems to me that the minister probably has the better grasp of constitutional propriety about it. He's moving in the right direction.
"In general, it seems to me that most judges would be upset this morning at going into court thinking that the public regards them as having a heightened sense of self-entitlement and concern about their status in society."
Kenny sees no need to intervene
Speaking in the Dáil, Taoiseach Enda Kenny has said the situation does not require his intervention.
In response to Fianna Fáil's Micheál Martin, Mr Kenny said he was happy to continue the extent of formal and informal engagement that takes place and facilitate through the Attorney General's office.
He said the independence of the judiciary was enshrined in the Constitution and was central to democracy.
Mr Kenny said clearly there were matters of concern to the judiciary with regard to a number of forthcoming measures and that it was only appropriate that there be proper consultation.
The Taoiseach rejected Mr Martin's assertion that the Government was demonising the judiciary.
Mr Martin has warned of the danger of a "full-blown Constitutional crisis".
Speaking at Leinster House, Mr Martin urged the Taoiseach to intervene, to "pull Alan Shatter back", and to reach out to judges.
He claimed that Minister Shatter's behaviour was "unacceptable" and asked why he always sees himself as being right.
Tánaiste Eamon Gilmore has described the judiciary as a cornerstone of Ireland's democratic process.
He said: "The Government respects the independence of the judiciary. It's a cornerstone of our democratic and judicial system.
"Frankly, I think it is a conversation that is best not conducted in public. I don't think dialogue over the airwaves is the way in which this type of discussion should take place."
Meanwhile, Minister for Transport Leo Varadkar said he supports his ministerial colleague Mr Shatter in the controversy.
Mr Varadkar said the issue is about the pay, pensions and privileges of judges.
He said a lot of judges are hurting because of the changes introduced by the Government.
While that is understandable, he said, they have to make their contribution to society.
He also dismissed the notion that this was a Constitutional crisis and said that the Government respects the independence of judges.