He was speaking at the launch of a number of housing projects in Cork
Simon Coveney has told Fine Gael TDs and Senators to 'back off' the Taoiseach, over the party leadership.
Minister Coveney and Leo Varadkar agreed at the weekend that Enda Kenny should be given until after St Patrick's Day to step aside.
Speaking today in Cork, the Housing Minister said the party must trust the Taoiseach to know what's best for the country.
Minister Coveney was in Cork today at the launch of a number of social housing projects in the city. He spoke to a number of reporters about the issue of Fine Gael party leadership.
Enda Kenny is set to address a Fine Gael Parliamentary Party meeting on Wednesday on the matter of party leadership.
For the most part, Coveney stuck to his guns and said that "we shouldn't be laying down ultimatums" for Enda Kenny. He said that he trusts him to manage a transition that's in the best interests of the country.
Coveney said what we need now is "a period of calm both in Government and in Fine Gael, where we put a bit of faith in Enda Kenny to manage a process that I except will start after St. Patrick's Day."
Meanwhile, three other senior Ministers have refused to rule themselves out of the running to succeed Enda Kenny.
Ministers Simon Harris, Frances Fitzgerald and Richard Bruton won't say if they'd run or not for Fine Gael party leader.
Minister Bruton says the party has to make a decision on the timing collectively.