Fine Gael leader Simon Harris has refused to be drawn on his intentions around a possible reshuffle of Ministers in his party.
He said that such decisions were "for another day".
Mr Harris told reporters that he would be speaking to all parliamentary party members, including outgoing Fine Gael TDs. to understand their reasons for stepping down and to ensure that they are happy with their decision.
Mr Harris spoke to Taoiseach Leo Varadkar to discus the transition of power, where he was briefed on upcoming national and international issues.
It was the first time that both of them have met since Mr Varadkar's resignation announcement last Wednesday.
Mr Harris is also due to meet the other Coalition leaders later this week, ahead of being elected Taoiseach by the Dáil on 9 April.
Asked if Mr Varadkar offered advice to him, the new party leader said that the Taoiseach told him that it was important to "be yourself and that every holder of office has to bring themselves and their own authenticity to the role".
Hate speech legislation
Mr Harris said that the controversial hate speech legislation was in the programme for Government.
It follows calls from Sinn Féin for it to be scrapped.
Sinn Féin spokesperson on Justice Pa Daly said that "it is abundantly clear that this legislation has been badly thought through and is not fit for purpose. It must not proceed".
Mr Daly said that the bill does not have support across the political spectrum, and he called on Mr Harris to clarify his position on the matter.
Mr Harris said that legitimate questions have been raised about the content of the legislation.
He said politicians should approach these issues with humility and that he would expect there to be revisions and amendments to the legislation.
Mr Harris was speaking at a "Future of Europe" conference, organised by MEP Frances Fitzgerald.
He also reiterated his belief that the Government should last its full term to March 2025.
Separately, the Cabinet is due to meet for its regular meeting on Wednesday and will be chaired by the Taoiseach.
Mr Harris told the media at a party event in Athlone that he believes the Coalition needs to focus on what it can get done, given that it only has one more year before a General Election must be called.
He said he wants to talk to all Fine Gael ministers in relation to what they believe they can deliver within that timeframe.
He added that he wants to discuss the implementation timeline of commitments in the Programme for Government with Fianna Fáil leader Micheál Martin and Green Party leader Eamon Ryan.
Mr Harris stressed that he believed the Coalition could continue to deliver if the leaders anchored their relationships in trust and mutual respect.
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Opposition parties are insistent that the best option would be for the Government to call a General Election now.
However, Mr Harris said he wants the Coalition to run its full term up to March 2025 which is an opinion supported by both Mr Martin and Mr Ryan.
Mr Ó Broin has said that that it was disappointing that Simon Harris did not focus on issues such as housing and health in his speech to Fine Gael members on Sunday.
Mr Ó Broin said: "We're in the middle of the deepest housing crisis in modern history. Homelessness is at record highs, rents and house prices continue to rise. Social and affordable housing targets are too low and are not being met.
"And did Simon Harris say that housing was going to be one of his key priorities as incoming Taoiseach? No, he did not."
Meanwhile, Fine Gael TD Brendan Griffin has said he has not changed his mind about not running for re-election.
