The Fine Gael parliamentary party yesterday decided against allowing any representations from party members at their meeting yesterday.
Mr Colm MacEochaidh, who ran as a candidate in Dublin South East, had asked to address the meeting.
He organised a meeting in Dublin on Tuesday night, which was attended by some 150 people, to protest at the leadership election being conducted without the grassroots being involved.
Party chairman Mr Padraic McCormack confirmed yesterday that Mr MacEochaidh and Mr Raymond O'Rourke, who ran as a candidate in Wicklow, had asked to address the meeting and he had passed on their request.
"But the party felt they couldn't create a precedent in allowing people outside the parliamentary party to address it, particularly a very important meeting like that."
Mr MacEochaidh said he "respected and accepted" the decision and congratulated Mr Enda Kenny on his election as leader.
He hoped that Mr Kenny would join the campaign that he had been part of, since the election, to reinvigorate the party.
"I hope his first action as leader is to engage with the grassroots and use their energies as the basis for his leadership. I would encourage all the people who are concerned about Fine Gael to join Enda Kenny in rebuilding the party."
Mr McCormack said he anticipated there would be an ardfheis in September and said that Mr Kenny was open to be "offered to the electorate, to any electoral system or to the ardfheis for ratification or otherwise".
But Mr MacEochaidh said while this was an interesting idea it "lacks a little credibility if only one candidate is being put forward and he is the party leader. There is little chance the party will say no."
Mr Leo Varadaker, constituency organiser for Dublin West, said last night that Mr Kenny also had his support as leader. However, he and other party members would "expect him to have achieved a lot by the time of the ardfheis in September".