Both contenders, Leo Varadkar and Mr Coveney, came face-to-face to debate in Dublin’s Red Cow Hotel last night.
More than 800 Fine Gael members packed into the ballroom, with supporters donning stickers for their favoured candidate and queuing to get onto the event.
The debate, which was streamed live on Facebook, was viewed by more than 100,000 people.
Moderator Gavin Duffy said that he had met both candidates before the debate and said they “have weighed in very well and are fighting fit”.
Mr Duffy said he did not envy Fine Gael members in the audience and around the country, as they are “blessed and burdened in equal measure” by being tasked with deciding between two high-calibre candidates.
The candidates clashed when differing views on the future of Fine Gael and who the party should appeal to were aired early on in the debate.
In his opening address, Mr Varadkar said that, under his leadership, Fine Gael “will stand for things and everyone will know what they are”.
He said party membership must be widened and the party needs to “open a conversation with those who have lost faith in us and those who have never considered voting for us”.
He added: “Being all things to all people is the Fianna Fáil way. Do that and we end up being nothing to anyone. We’ve tried it many times in the past and remained in opposition as a result.”
In a thinly veiled attack on his opponent, Mr Coveney said “of course we need to help people who get up in the morning”, but he went on to say that Fine Gael must also help people who cannot get up in the morning, who need assistance and motivation.
“The party that I love is about make a a choice between two view points; I am deeply passionate about one and deeply concerned about the other,” he said.
“We have to represent the man in the sleeping bag on Grafton Street tonight, as well as the man creating 1,000 jobs.”
Mr Coveney said that the man in the sleeping bag may never vote, but it was still right to help him and other vulnerable people.
“Society in Ireland has lost faith in politics and each political party is targeting different segments in society, which is driving people apart,” Mr Coveney said, stressing the need for unity.
The housing minister admitted to being the clear underdog in the race.
“I am not used to that position, and I’m not overly happy about it either,” the Corkman said to loud applause.
“Underdog or not, I intend on carrying a powerful message, which is what I am about in politics. What you see is what you get.”
Dubliner Mr Varadkar sought to land a blow on his rival, saying there had been three months to prepare for the leadership race and, as taoiseach, the successful candidate might not have the luxury of that length of time to prepare for a general election.