Michael D Higgins used his re-election speech last night to call for an end to the "scourge of violence against women".
The President promised to represent everybody in the country, regardless of whether they voted for him or not.
And in a thinly veiled reference to the debate about the Traveller community which dominated the campaign, Mr Higgins said: "Words matter. Words can hurt. Words can heal. Words can empower. Words can divide."
He promised to identify those facing exclusion in society, which he said was "more than just eliminating barriers, it means the exercising of new initiations."
He continued: "A real Republic is a Republic of equality, of shared vulnerabilities and of collective capacities.
"A real Republic is one where every person is encouraged and supported to participate fully and where every person and community is treated with dignity and respect."
The 77-year-old received the largest ever mandate in the history of the State, albeit from the lowest ever turnout in a presidential election.
He received 822, 566 votes, amounting to 55.8pc of the vote.
Standing in front of his five rivals at Dublin Castle, Mr Higgins said he campaigned on "values which the Irish public have now overwhelmingly chosen as reflecting what they believe to be the important and necessary basis for Ireland and our future.
"The Presidency of Ireland draws its strength and independent mandate from the direct vote of the people of Ireland. It represents Ireland - in all our strengths and vulnerabilities," he said.
However, he said the country is "now in a time of transformation" and through the presidency he hoped to allow "an independent space where new ideas and possibilities can emerge".
Mr Higgins noted that the years ahead will see the commemoration of "challenging, often difficult, periods of our history" including the centenary of the first Dail next year.
"This task will require sensitive thought, reflection and understanding - an ethics of memory and a narrative of hospitality, enabling different versions of shared events to be placed side by side, uncomfortable truths acknowledged."
Over the next years in Aras an Uachtarain, the President said he would represent "Ireland's voice, as we face challenges that are global".
"The urgent need to end the scourge of violence against women cannot be deferred, but must be ended now," he said to applause.
"I will, on your behalf, represent an Ireland committed to a peaceful world and a shared planet - and together we will ensure that Ireland's voice matters.
"This is a time to be active rather than passive, and clear choices are opening up as to what will be the character of our Irishness."
He concluded, saying the country had voted for "the making of hope" rather "than the experience of any exploitation of fear".
"I will be a President for all the people, for those who voted for me and those who did not. I am so proud of our country, I am proud to be a President for all of you and with all of you, and I look forward with joy and hope to all that we will achieve together."
The defeated candidates congratulated Mr Higgins after his speech and all expressed no regrets about entering the campaign.
Senator Joan Freeman said she wanted to remark on the "courage of the candidates".
"It's not easy to have yourself scrutinised, criticised and sometimes brutalised.
"But I think we showed great courage and at the end of it I want to have a glass of wine with them at some stage just to share and just to talk and just to see what it was like for all of us."
Peter Casey, who finished second and spoke directly after Mr Higgins, said: "I hate following a great orator - one of the best... In the words of Elizabeth Taylor to her seventh husband: 'I won't be keeping you long'."
He said his vote of more than 342,000 was a 23,000pc improvement on the 13 votes he got in the 2016 Seanad election.
Businessman Sean Gallagher wished Mr Higgins every success in the next seven years.
He called for a focus on opportunity over cynicism in Ireland.
He said: "Cynicism does not create change. Positive change only comes from challenging the status quo.
"To achieve this we need new ideas driven by brave people who are willing to step into the arena rather than commentate from the sidelines.
"As Teddy Roosevelt said, it is not the voice of the critic that counts. The credit goes to the man who is actually in the arena whose face is marked with dust and sweat and blood."