The Vatican announced the Pope's death this morning.
President Higgins said that the pontiff "sought to show in the most striking and moving of ways, the extraordinary importance of the spiritual" as a powerful source of global ethics in the challenges of contemporary life".
He said that Pope Francis' voice constituted a "consistent invocation of a shared humanity" and he was vocal on the "vital issues of our time" including global hunger, poverty, climate change and justice.
"These issues I had the privilege of discussing at length with Pope Francis across our five meetings over the course of his Papacy," he said in a statement.
"During his visit to Ireland, Pope Francis spoke of the scandal of child abuse, including in the Church, and its consequences for victims and families. On such matters, and on others such as attitudes towards women and those of the LGBTQ+ community within the Church, Pope Francis sought to play a positive role," the President said.
"I recall at the end of our meetings he would say as to his work on such issues, 'it is very difficult', as he asked for and offered prayers. It is important that the steps he took are built upon as they constitute a source of hope in the years to come."
A legacy of peace
Taoiseach Micheál Martin said that Pope Francis' legacy is "his message of peace, reconciliation, and solidarity that lives in the hearts of those he inspired".
In a statement, the Fianna Fáil leader said that Pope Francis "long and distinguished papacy was marked by his unwavering commitment to the principles of compassion, peace, and human dignity".
"He spoke out for the poor, the marginalised, and the oppressed. His solidarity with refugees, his calls for climate action, and his insistence on global peace and equality set him apart as a champion of justice in the modern world.
"On behalf of the Government and the people of Ireland, I offer my heartfelt sympathies and my deepest condolences to all who mourn him, to His Eminence Cardinal Battista Re, the Dean of the College of Cardinals, to his family and friends and to the Catholic community worldwide that has lost an exceptional leader."
Mr Martin said that Pope Francis holds a "special place in the hearts of the Irish people".
"During his visit to Ireland in August 2018 for the World Meeting of Families he was welcomed with a warmth and enthusiasm that spoke volumes about the respect and affection in which he was held by Irish people," he said.
"Many will also remember Pope Francis' expression of pain and shame about historic child abuse in the Catholic Church and his outrage about the failure of Church authorities to adequately address these appalling crimes."
Pope's influence 'transcended the Vatican'
Tánaiste Simon Harris said the Pope's influence "transcended the Vatican", adding that he offered "moral leadership during times of uncertainty".
In a statement, the Fine Gael leader said that his teachings on poverty, migration, and refugees "remain relevant as we confront global inequality and division".
Mr Harris said Pope Francis was a "remarkable figure who embodied compassion, humility, and service". "On behalf of the people of Ireland, I offer my condolences to His Eminence Cardinal Battista Re, Dean of the College of Cardinals, the entire Roman Catholic Church, and all those mourning his loss worldwide.
"Pope Francis bore his illness with great dignity and courage. As so many people in Ireland and as Christians across the world mourn his loss, we find strength in his message of hope, mercy, and compassion, which will continue to inspire us to build a better world for all."