Fianna Fáil leader Micheál Martin said the party's strong performance was due to staying grounded and having a message that resonated with people.
There was a jubilant atmosphere in the concert hall of Cork City Hall as Fianna Fáil had two TDs elected in the first count.
Party leader Micheál Martin and Michael McGrath were hoisted onto the shoulders of cheering supporters who had packed out the grand hall to hear the result for the Cork South Central constituency.
Both men, who were surrounded by their families, waved and punched the air in delight as the figures were announced.
Fianna Fáil leader Micheál Martin and his party colleague Michael McGrath have been re-elected in Cork South Centralhttps://t.co/cISrUt4c4R
— RTÉ News (@rtenews) February 27, 2016
When they were eventually brought back to down to earth, there were kisses and hugs aplenty.
But, as the barely audible returning officer concluded, one elderly Fianna Fáil voter quipped: "The real work begins now, lads - from today."
Mr Martin, who polled 11,346 votes, attributed his party's success to staying grounded.
He said: "It just shows, if you set yourself a challenge there is no reason why you can't win.
"I think there were a lot of things worked in our favour. We had faith going way back. We were consistent and the local elections gave us a great platform. Our message resonated with people.
"I think we kept our feet on the ground; we connected with communities and that will be the strongest challenge - to stay connected with people and their realities on the ground."
Earlier, the count centre had erupted into applause when Mr Martin arrived amid a flurry of photographers' flashes.
At one point he was even asked to sign autographs.
However, he declined to be drawn on the prospect of a so-called "grand coalition" with Fine Gael.
"We have made it clear we do not want to go into government with Fine Gael or with Sinn Féin," he said.
"We have got to see the final destination of these seats because I think a lot of centre-ground people are going to be elected as well and I think a lot of them are sensible, and I think we can't ignore that.
"They also have responsibilities. The idea that it is just down to two parties, I think, is ignoring the reality of how people voted.
"We will have a certain number of seats that enables us to do certain things and enables us to take certain positions, but it is by no means the dominant position in the Dail."
Mr McGrath, who topped the poll with 11,795 votes, described it as a "great honour" to be returned with such a mandate.
He said: "I am absolutely delighted with the outcome of Cork South Central and I really want to thank all the people that voted for me. I am really overwhelmed by the support."
Mr McGrath added that the onus was on everyone to create a stable government.
The party's General Secretary has said that it is on track to take over 40 seats but it is hard to be definitive.
Seán Dorgan said the party has made up phenomenal ground over the last number of years.
He said candidates were in contention for a seat in every constituency outside of Dublin and in most of the Dublin constituencies and was rapidly closing the gap with Fine Gael.
Éamon Ó Cuív, who topped the poll in Galway West, believes that the electorate are giving Fianna Fáil a tentative approval rating.
He said the government has taken a beating and if Fine Gael, who have had a "disastrous" election, are put back into power the electorate will say that they have been cheated.
Mr Ó Cuív said he always believed Fianna Fáil would bounce back and Mr Martin had led the party in a strong campaign and was a stand-out leader during the television debates.
