Taoiseach Leo Varadkar has said the confidence and supply arrangement between his party and Fianna Fáil did not require the Government to "run" judicial and public appointments by them.
"We have a written agreement," Mr Varadkar said at his first summit of EU leaders in Brussels.
"That written agreement does not require that we run appointments - either judicial appointments or public appointments - by Fianna Fáil, nor could it, so I don't believe that there has been a breach of the confidence and supply agreement."
Mr Varadkar said both parties should "work closely" in the coming weeks, and to have "confidence building measures."
Meanwhile, Fianna Fáil leader Micheál Martin will not be withdrawing remarks made in the Dáil about the appointment of Máire Whelan to the Court of Appeal, according to the party's Spokesperson on Public Expenditure and Reform.
Dara Calleary said focusing on Mr Martin's remarks was just a distraction from the core element of this issue, which was the process by which the former attorney general was appointed to the Court of Appeal.
Speaking on RTÉ’s Morning Ireland, he said the appointment process had been flawed and arrogant and that Fianna Fáil is unconvinced that the appointment was lawful.
Mr Calleary said a phone call between the Fianna Fáil leader and the Taoiseach was not an attempt to influence the appointment, but for Mr Martin to express his concerns over the appointment and the process by which it was made.
He said it would be unusual for Mr Martin to make such a phone call because the party "didn't like bringing things to drama".
He added that the appointment process, and not the phone call, was the problem.
Mr Calleary said there were processes within the confidence and supply agreement to deal with disagreements like this.
Last night during a Dáil debate on the controversy, opposition parties said that the correct procedures concerning Ms Whelan's appointment were not followed.
Tánaiste Frances Fitzgerald defended the appointment, describing it as a Government prerogative.
The Dáil debate lasted more than two hours but at the end of it many questions asked by TDs remained unanswered.
Several wanted to know how many others had applied to become a judge at the Court of Appeal.
Ms Fitzgerald could only say that all applications for such posts are considered and treated in a confidential manner.
When asked who made the decision to bring Ms Whelan's name to Cabinet, the Tánaiste said it is the norm in these cases for the Minister for Justice in consultation with the Taoiseach to do so.
However, she said she did not have any discussion with Leo Varadkar about the appointment.
Fianna Fáil's Jim O'Callaghan said it was laughable to suggest the Government had followed correct procedures.
Sinn Féin said the Government had wilfully circumvented the law.
The Tánaiste insisted, however, that Ms Whelan's six years of experience as attorney general ensured she was qualified to become a judge at the Court of Appeal.