Mary Lou McDonald says it's unacceptable that government is refusing to allow the Justice Minister answer Dáil questions about it.
Helen McEntee's under pressure to appear before TD's to explain why the Taoiseach and Cabinet weren't informed of other candidates who applied for the position.
Yesterday, Minister McEntee defended her actions, saying she spoke to the three party leaders and the attorney general before issuing a recommendation.
However, Mary Lou McDonald says her explanation isn't good enough:
"I think that's a patchy explanation that and it contradicts the fact that both the Taoiseach, and the leader of the Green Party have said on the public record that they were unaware that there were three additional expressions of interest from members of the judiciary for this appointment to the Supreme Courts. So matters are in dispute."