President Michael D Higgins has congratulated president-elect Catherine Connolly on her election victory, while several senior politicians said a response is needed to the 213,738 spoiled votes.
Ms Connolly received just over 63% of first preference votes and was elected on the first count.
Her opponent in the race, Fine Gael's Heather Humphreys, secured just over 29%.
The Galway West TD's victory in the election will trigger a by-election in the constituency to fill her seat, which must be held within six months of her inauguration as the tenth President of Ireland.
Following her election victory, President Higgins said Ms Connolly will have the full support of his office as she prepares for her inauguration on 11 November.
In a statement, President Higgins said: "I have this evening spoken by telephone with the president-elect, Catherine Connolly. I congratulated the president-elect on her election as the tenth President of Ireland on what is a momentous day for her and her family.
"The president-elect will have the full support of this office as she prepares for her Inauguration next month."
Taoiseach Micheál Martin said he looked forward "to working with the new president", while Tánaiste Simon Harris said "today is her day" in relation to Ms Connolly.
Members of the political parties who backed Ms Connolly's campaign, including the Green Party, Labour, People Before Profit-Solidarity, Sinn Féin, and the Social Democrats, also congratulated the Galway West TD.
'Voice for peace'
In her victory speech last night, the president-elect vowed to be an "inclusive" president for all.
Speaking at Dublin Castle, she said: "I will be a voice for peace, a voice that builds on our policy of neutrality, a voice that articulates the existential threat posed by climate change, and a voice that recognises the tremendous work being done the length and breadth of the country.
"Our whole mantra during this campaign was that we can shape a new Republic together and we can use our voices for those who haven't the ability, or for whom the circumstances don't allow it."
Watch: Catherine Connolly says she will be an 'inclusive' president for all
However, the presidential election was also marked by a significant number of spoiled votes, with 213,738 invalid polls nationwide.
It represents 13% of all votes cast on Friday and a more than tenfold increase on the number of spoiled votes in the last presidential election in 2018, when there were 18,438 invalid ballots.
The turnout was 46%, up on the 2018 presidential election which had a turnout of 44%.
An Coimisiún Toghcháin said there "will clearly be a need for deeper and further reflection" about why there were so many spoiled ballots in the election.
It added that the number of spoiled ballots was "significantly higher than normal", adding that is "clear that some people chose to deliberately spoil their votes".
In the Dublin Mid-West constituency, 21% of votes cast were spoiled.
Read more: Opposition hoping Connolly win paves way for Govt change
Many had an "X" or slash drawn through all three candidates, or the words "spoiled" or "spoilt" written on the slip.
There were also a significant number of spoiled votes with anti-Government messages, including "no democracy", "EU puppets" and "no from me".
A number of names were also written on many invalid ballot papers in the count centre in Adamstown, including Maria Steen, who tried to become a presidential candidate but failed to get enough nominations by the deadline.
Sinn Féin Dublin Mid-West TD Eoin Ó Broin said the spoiled votes meant that 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," he said.
Speaking at Dublin Castle, the Tánaiste also expressed concern about the high number of spoiled ballots.
He said some voters put "quite a lot of effort in spoiling their ballot", adding that it showed "the number of people in Ireland now who are clearly feeling disaffected or disconnected with politics".
People Before Profit-Solidarity TD Paul Murphy said he did not think it was a "moral failing" to spoil votes, and that it was a "legitimate choice that people can make".
When spoiled votes were excluded, Fianna Fáil's Jim Gavin, who withdrew from campaigning, secured 7% of first preference votes.
Of the 3,612,957 people eligible to vote, 1,656,436 cast their vote in the 2025 presidential election, representing a turnout of 46%.
