Minister for Social Protection Leo Varadkar has said Minister for Housing Simon Coveney is someone for whom he has immense regard, who is very diligent, very serious and a very persistent politician.
"I'm sure no matter what way party members vote next week, we'll be able to work together and get on with things in the interest of the country," Mr Varadkar said
Asked if he is concerned that people may change their minds and support Mr Coveney, he said a large number of people have made declarations supporting him.
"Making a declaration isn't just saying you're going to support somebody, it's signing a piece of paper, it's nominating a candidate, sending it to headquarters so I think it would take a lot for an individual to withdraw a declaration," Mr Varadkar added.
Minister for Defence Paul Kehoe has said that he is not for turning and he will not be changing his mind in relation to his support for Mr Varadkar in the leadership contest.
Speaking in Cork, Mr Kehoe said he had nailed his colours to the mast by declaring his support for Mr Varadkar.
He was responding to a question in relation to Mr Coveney's expressed hope to persuade half a dozen Oireachtas members to change their preferences, even though they had already pledged their support to Mr Varadkar.
Meanwhile, the Minister for Housing was among many Irish politicians to express sympathy following the tragic attack on a concert in Manchester which has killed at least 22 people.
Speaking to RTÉ News Mr Coveney said "it's so close to home, so many Irish people living in Manchester.
"I think what you'll see from the Irish Government and other sources will be words of solidarity, trying to reach out on a very, very sad day."
Taoiseach Enda Kenny and President Michael D Higgins were also among the many Irish politicians sharing their condolences.