Irish premier Micheal Martin has led tributes to the Duke of Edinburgh.
Philip died at the age of 99, Buckingham Palace announced on Friday.
The Taoiseach was among a number of Irish politicians to express their condolences after his death.
Mr Martin said: “Saddened to hear of the death of HRH Prince Philip, Duke of Edinburgh.
“Our thoughts and prayers are with Queen Elizabeth and the people of the United Kingdom at this time.”
Ireland’s Foreign Affairs Minister Simon Coveney said: “I want to express sincere condolences to all British people on the sad passing of His Royal Highness Prince Philip, Duke of Edinburgh.
“Our thoughts and solidarity are with you on a very sad day for the United Kingdom.”
The Queen and Prince Philip made their first State visit to Ireland in 2011.
The historic four-day visit was the first to the Republic of Ireland by a reigning British monarch.
Irish President Michael D Higgins also expressed his “great sadness” at the duke’s death.
“On behalf of the people of Ireland, I wish to convey my condolences to Her Majesty Queen Elizabeth, her children, her extended family and the people of the United Kingdom,” he said.
He added: “For over 60 years, and as husband to Britain’s longest serving monarch, Prince Philip served the British people with an unfailing commitment and devotion to duty.
“In the course of his long service he frequently brought an air of informality to otherwise formal occasions.
“His distinctive presence and unique sense of humour put participants at ease and always engaged those who encountered him.
“Prince Philip was a steadfast support to Queen Elizabeth II.
“He accompanied the Queen on her many visits to Northern Ireland and also on her historic State Visit to Ireland in 2011.
“I recall with a special appreciation how welcome he made Sabina and I feel in 2014, when I was making the first State Visit by an Irish Head of State to the United Kingdom in 2014.
“My hope is that these visits in 2011 and 2014, which he shared, will continue to be symbols of what we share as neighbours in friendship, peace and a sustainable future.”
He added the Irish saying “Ar dheis De go raibh a anam dilis”, meaning may his holy soul be on the right side of God.
Sinn Fein leader Mary Lou McDonald said: “Sincere condolences to Queen Elizabeth and family on the death of her husband Prince Phillip.
“Sympathies to those of a British identity on our island, for whom his death will be felt as a great loss.”
The head of the Catholic Church in Ireland expressed his sympathy to Queen Elizabeth on the death of the duke.
Archbishop Eamon Martin said he was saddened to hear of the death of Philip.
“Prince Philip has been a regular visitor to Northern Ireland in connection with his widespread charitable work,” he added.
“Many pupils from right across the community here have participated in the Duke of Edinburgh Award Scheme.
“However, his visit to Ireland along with Queen Elizabeth in 2011 stands out as a cherished moment of peace and reconciliation and as an historic demonstration of the importance of mutual understanding and respectful relationships between these islands.
“I will offer prayers for Queen Elizabeth and her family at this difficult personal time and will pray for the happy repose of the soul of Prince Philip.”