Heather Humphreys has congratulated Catherine Connolly as she looked secure to become the next president of Ireland by a significant margin.
Ms Connolly said earlier on Saturday that she was “absolutely delighted” with tallies indicating she is the clear victor.
The electorate had the choice between left-wing independent Ms Connolly, former cabinet minister Heather Humphreys and ex-Dublin football manager Jim Gavin, until he withdrew from campaigning three weeks ago.
From early on Saturday, Ms Connolly was ahead in count centres nationwide.
There also appeared to be a significant number of spoiled votes.
Speaking to reporters at the Cavan-Monaghan count centre, Ms Humphreys said: “Catherine will be a president for all of us and she will be my president, and I really would like to wish her all the very, very best.
“I have absolutely not one regret.”
Speaking to reporters in Galway earlier on Saturday, Ms Connolly said: “I am absolutely delighted with the result and I want to thank all my supporters.
“Actually, I want to thank everybody – even those who did not vote for me.
“I understand their concerns in relation to who will represent them best.”
As ballot boxes opened and votes are sorted ahead of the official count, activists and volunteers observe the process to form unofficial tallies.
These calculations put Ms Connolly on path for victory, with different regions putting that candidate on between 50-75% of the vote.
There were also a significant number of spoiled votes with anti-Government messages on them, including “no democracy”, “EU puppets” and “no from me”.
Among the messages on spoiled votes were “Maria Steen”, who failed to get enough nominations to become a candidate, and references to an alleged sexual assault on a 10-year-old girl that sparked anti-immigration demonstrations in west Dublin this week.
Local Sinn Fein TD Eoin O Broin said the scale of the vote for Ms Connolly was “very, very significant”.
He added: “A huge Catherine Connolly vote here, an absolute collapse not just of the Fianna Fail vote – and that was to be expected – but of the Fine Gael vote as well, (which is) really remarkable in a constituency where Fine Gael used to have two TDs and currently have a sitting junior minister.
“And then of course there is a significant number of spoils, you can’t deny that. And what it tells us is there are people out there who are very angry, who are very unhappy.
“Our job in the time ahead is to try and convince more of those people that there is an alternative, there is a message of hope, and we hear the fact that they are not happy. So there is a job of work to do afterwards.”
Aontu leader Peadar Toibin has revealed he spoiled his vote for the presidential election.
Speaking to reporters at the RDS Simmonscourt count centre, Mr Toibin said: “I’m going to be brutally honest with you, and I feel weird even saying this, I spoiled my vote yesterday.”
Mr Toibin said he drew three Xs beside the candidates and wrote in the name of Ms Steen instead.
People Before Profit TD Paul Murphy claimed Ms Connolly will win the Irish presidency “by the biggest margin ever of any presidential election”.
Speaking to the PA news agency at Dublin Castle, Mr Murphy described the election as “historic”, adding this will be the “first national election where the left will have won over 50% of votes on first preferences”.
The winner of the election will replace Michael D Higgins, a popular poet and former arts minister who has served the maximum two terms in office.
Voting slips will be counted by hand at more than 30 count centres, representing 43 electoral constituencies, across the country.
Ireland uses a system of transferable votes in elections but, with only three candidates on the ballot, there can only be a maximum of two counts.
The final result will be officially declared by presidential returning officer Barry Ryan once all 43 constituencies have completed counting.
The leader of the Irish Labour Party said Ms Connolly has united parties “with an alternative vision”.
Ivana Bacik said left-wing parties could now look at how they can “combine together” and “offer a real alternative” in the next general election.
Asked about the high number of spoiled votes, Ms Bacik said: “The level of vitriol directed at people of all political persuasions on some of those spoiled ballots is really alarming to see and I think it means we need to take that anti-democratic threat really seriously.”
In the weeks before polling day, several opinion polls put Ms Connolly ahead of Ms Humphreys by some margin.
Ms Connolly cast her vote at a primary school in Claddagh, Co Galway, on Friday after going for a swim that morning.
She took time after voting to examine students’ essays about the presidency that were pinned to the wall, and to take her elderly aunt, who was in a wheelchair, into the polling station, before cycling home.
Ms Humphreys cast her vote in Newbliss, Co Monaghan, with daughter Eva and one-year-old granddaughter Charlotte.
Mr Gavin withdrew from campaigning after the emergence of a 16-year-old dispute with a former tenant.
The ex-army pilot, 54, who was best known for his role as the manager of Dublin’s record-breaking Gaelic football team, which won five successive All-Ireland Championships, withdrew from the race three weeks before polling day.
It came after a former tenant, deputy editor of the Sunday World Niall Donald, claimed he tried to recover 3,300 euro in overpaid rent from Mr Gavin.
Mr Gavin said he had made a mistake “not in keeping with my character” and repaid the money after his withdrawal.
The move has had serious implications for the Fianna Fail party, which selected him as their candidate, and for its leader, Taoiseach Micheal Martin, who championed Mr Gavin.
It also had an effect on the election count as his late withdrawal meant there was not enough time to legally remove his name from the ballot paper.
If he had won the most votes, he would still be elected as president.
It is a largely ceremonial role which involves hosting heads of state at the president’s official residence, Aras an Uachtarain in Phoenix Park, and other diplomatic and civic engagements.
The president must also consider whether legislation passed by the parliament complies with the constitution, and if they believe it does not, in consultation with the Council of State, they can refer it to the Supreme Court.
In recent years, the Irish presidency has become a more political role.
During his tenure, Mr Higgins said Ireland’s housing crisis was “our great, great failure”, that the UN was “losing credibility”, and that the Irish state must “urgently meet the needs of”, and address the concerns of, the survivors of mother and baby homes.
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