Simon Coveney boldly predicted he expects to win over the support of the Fine Gael TDs who have not publicly stated their voting intentions in the party's leadership race.
Mr Coveney did not name individuals, but those who have not yet declared include Taoiseach Enda Kenny and Finance Minister Michael Noonan.
In total, seven Fine Gael parliamentary party members remain undeclared.
Mr Coveney refused to comment on whether he was still working on securing the vote of Agriculture Minister Michael Creed, who has not stated his voting intentions and is the only other Cabinet minister from Cork.
Speaking before a campaign rally in Cavan, Mr Coveney said: "Michael Creed isn't the only person who has done that. There are a number of others as well and I think I will do pretty well among that group of TDs who have decided to keep their voting intentions to themselves."
The Housing Minister also predicted he would win the support of the membership by beating Leo Varadkar in all four leadership debates due to take place in the coming days.
He said he was having private conversations with TDs and senators who have pledged to vote for Mr Varadkar, but refused to give the names of those he has spoken with.
"I think I need to win back some of them but I'm not going to start naming names publicly and then start putting them under the spotlight of huge pressure, that wouldn't be a very clever strategy from my point of view," he said.
Meanwhile, Mr Coveney received a much needed boost as undeclared Fine Gael MEP Mairead McGuinness attended his leadership rally.
Ms McGuinness arrived late to the event and sat in the audience listening to contributions from Mr Coveney and his supporters.
Mr Coveney thanked the MEP for attending and joked he would not praise her too much as he would be accused of canvassing her.
Ms McGuinness later addressed the crowd saying she would not be declaring before the leadership hustings later this week.
Current Health Minister Simon Harris told the event that pundits who are writing off Mr Coveney's chances are the same people who said Brexit would not happen and Hillary Clinton would win the US presidential election.
Fine Gael parliamentary party endorsements for leader
The Fine Gael parliamentary party makes up 65pc of the total electorate.
That makes each of the 73 members' votes worth 0.9pc of the total ballot.
Of the remaining electorate, 230 party councillors account for 10pc, while the remaining 25pc is rank and file members.
|Richard Bruton -Minister||Simon Harris - Minister|
|Frances Fitzgerald - Minister||Damien English - Minister|
|Michael Ring - Minister||Dara Murphy - Minister|
|Eoghan Murphy - Minister||David Stanton - Minister|
|Sean Kyne - Minister||Marcella Corcoran Kennedy - Minister|
|Joe McHugh - Minister||Kate O'Connell - TD|
|Helen McEntee - Minister||Maria Bailey - TD|
|Charlie Flanagan - Minister||Sean Barrett TD|
|Paul Kehoe -Minister||Hildegard Naughton - TD|
|Patrick O'Donovan - Minister||Peter Fitzpatrick - TD|
|Regina Doherty - Minister||Tim Lombard - Senator|
|Mary Mitchell O'Connor - Minister||Jerry Buttimer - Senator|
|Paschal Donohoe - Minister||Paudie Coffey - Senator|
|Heather Humphreys - Minister||James Reilly - Senator|
|Pat Breen - Minister||Colm Burke - Senator|
|Catherine Byrne - Minister||John O'Mahony - Senator|
|Andrew Doyle - Minister||Paul Coghlan - Senator|
|John Paul Phelan - TD||Gabrielle McFadden - Senator|
|Noel Rock - TD||Deirdre Clune - MEP|
|Tony McLoughlin - TD|
|Alan Farrell - TD|
|Michael D'Arcy - TD|
|Tom Neville - TD|
|Josepha Madigan - TD|
|Pat Deering - TD|
|Jim Daly - TD|
|Brendan Griffin - TD|
|Ciaran Cannon - TD|
|Colm Brophy - TD|
|Peter Burke - TD|
|Fergus O'Dowd - TD|
|John Deasy - TD|
|Joe Carey - TD|
|Neale Richmond - Senator|
|Catherine Noone - Senator|
|Paddy Burke - Senator|
|Martin Conway - Senator|
|Michelle Mulherin - Senator|
|Maura Hopkins - Senator|
|Ray Butler - Senator|
|Frank Feighan - Senator|
|Maria Byrne - Senator|
|Joe O'Reilly - Senator|
|Kieran O'Donnell - Senator|
|Brian Hayes - MEP|
|Enda Kenny - Outgoing Party Leader *||Martin Heydon - Party Chairman *|
|Michael Noonan - Minister||Michael Creed - Minister|
|Bernard Durkan - TD||Sean Kelly - MEP|
|Mairead McGuinness MEP|
* Outgoing leader Enda Kenny and party chairman Martin Heydon will not make an endorsement
There are few more unedifying sights in politics than a leadership contest. First off, there's the excruciating stuff the candidates have (or feel they have) to do - 'coffee or a 5km run anyone? Oh and, by the way, you have met my family, haven't you?'