Justice Minister Charlie Flanagan remains optimistic that Fine Gael will secure two seats in Ireland South.
Exit polls indicated that MEP Deirdre Clune could be facing a difficult fight to retain her seat in the constituency.
Her running mate Sean Kelly is expected to top the poll and colleague Andrew Doyle was reported to have secured about 4% of the vote.
Mr Flanagan said the potentially significant number of transfers from these two could make the difference to Ms Clune's chances.
"The only evidence I have is that which was contained in the exit poll. If the figures are precisely as of the exit poll, then I would give Deirdre Clune a very good chance to take the second seat for Fine Gael," Mr Flanagan said.
My understanding is that Sean Kelly will be on or above the quota - probably a little over it - which, in the circumstance, is very encouraging.
"It is a great vote for Sean, he is a great vote getter and has been a very good MEP. I would be concerned to ensure that we would get two seats here.
Andrew Doyle, up on the Leinster side, will have a significant number of votes to go to Deirdre Clune, assuming that Sean Kelly will be elected."
Mr Flanagan said that the differences between the exit polls and the results in Dublin have the party in a more confident mood.
"There was something of a differential between the exit poll and the votes," he said.
"If that is the case here, then everything is to play for."