Sinn Féin TD Pa Daly is taking legal action challenging the attendance of junior ministers at cabinet meetings.
Lawyers for Mr Daly told the High Court they were seeking a "very urgent" hearing of his application for permission to take the challenge.
The court was told the application for leave to seek judicial review relates to the appointment of ministers of state with rights to attend meetings of the Cabinet.
Senior Counsel Feichín McDonagh told Ms Justice Mary Rose Gearty that Mr Daly wants declarations that their attendance by virtue of the Government's designation is unconstitutional.
The so called "super juniors" who have been appointed, are Hildegarde Naughton of Fine Gael as well as Seán Canney and Noel Grealish of the Regional Independent Group.
Fianna Fáil’s Mary Butler has been appointed Government Chief Whip as well as a junior minister with responsibility for Mental Health.
Mr Daly, who is represented by Mr McDonagh as well as barristers Brendan Hennessy and John Biggins, and solicitor John Rogers, is taking his action against the Taoiseach, the Government, Ireland and the Attorney General.
He said the Constitution limits the number of Government ministers to 15 and binds them to confidentiality about their discussions. The attendance of extra ministers of state is not contemplated by the constitution, he said.
Mr Daly claims the Taoiseach and Government have failed to act in accordance with the democratic process. He said they can hold a referendum to amend the Constitution if they want to increase the size of Government.
The first time the practice of appointing "super junior" ministers occurred was during the 1994 "Rainbow Coalition" of Fine Gael, Labour and Democratic Left, when Pat Rabbitte was permitted to attend cabinet meetings.
Mr Daly said it appears the practice has continued since then, but it is inconsistent with the Constitution.
Ms Justice Gearty will hear the application for permission to take the legal challenge tomorrow afternoon.
