Green Party deputy leader Catherine Martin has accepted Agricultural Minister Barry Cowen's apology for his drink-driving offence.
Speaking on RTE's Radio 1 Morning Ireland, she said Minister Cowen had made a "serious mistake" and "hopefully he has learned from it."
However, she conceded that questions remain about why Minister Cowen was still driving on a learner permit at the age of 48.
"I think that is the one issue that wasn't addressed last night, yes I think he may have to reach out to them (road safety campaigners) and explain that himself."
Speaking about her challenge for leadership of the Greens, Ms Martin said: "The leadership election arises our party's constitution and it is a reminder of the vital role that democracy plays in our party.
"I think this is less about a challenge and more about a healthy conversation, a conversation about the present and more importantly the future direction of a very different party to where we were in 2011."
When asked if more women should have been promoted to Cabinet, the Minister for Media, Tourism, Arts, Culture, Sport and the Gaeltacht said that "young girls cannot be what they do not see".
She said: "I would always seek to promote women in our party but having said that all the Green Party Ministers who are there are good for the job and I respect the decision there, that was the prerogative of Eamon as leader but I do feel forever we have women who have proven they're ready and very able, then we should always seel to promote because young girls cannot aim to be what they cannot see and we should always be seeking to do that to promote women.
"In relation to the male ministers, I congratulate them and they're all able for the job, I think there was a missed opportunity to promote women and from our side there was a missed opportunity to unite the party as well.
"Nobody that voted no or advocated no to the Programme for Government was promoted to a ministerial position and I think there was a missed opportunity to unite.
"We are a party that respect and cherish debate and challenge and having those voices heard inside within Government and at a ministerial table would have been welcome, I think."
Commenting on remarks made by fellow party member Lorna Bogue about "ingrained type of misogyny" in the Greens, Ms Martin said: "I think we have to be seen to do more as a party, we talk the talk in relation to promoting diversity and inclusivity but if we're not acting on it I think that's regrettable and that's something I would like to see change."
