Leo Varadkar has secured the abstention of Fianna Fáil which should all but guarantee his election as Taoiseach in the Dáil next week.
However, he also wants confidence in the administration of justice restored.
The Fine Gael leader met with Micheál Martin this afternoon as part of a round of meetings to secure enough votes to replace Enda Kenny at the helm.
Mr Martin has told reporters this afternoon he raised several issues with Mr Varadkar especially in health and housing where more needs to happen, and he wants confidence in justice restored.
Mr Martin said: "I made it clear to the minister that while the Confidence and Supply Agreement does not, of course, involve me or anybody telling him as an incoming Taoiseach who he would appoint to a ministerial Cabinet or indeed any of those matters.
"We made it clear that was not our function, but that the overarching objective of his government will have to be the restoration of confidence in the administration of justice and policing in this country."