President Michael D Higgins has said that his attendance at the coronation of King Charles III reflects a "significant break" from the past and demonstrates what is required in terms of good relations between countries.
King Charles III was crowned in Britain's biggest ceremonial event for seven decades.
Mr Higgins is the first Irish head of state to attend a coronation.
Mr Higgins said that 70 years ago, when Queen Elizabeth had her coronation, Irish people were encouraged not to listen to it on the radio.
"It is very important in terms of being able to draw the distinction between what is at the top end of the courtesies required of good relations between countries," he said.
Mr Higgins said that in the UK the monarchy is regarded as a symbol of stability in a country without a constitution.
"The relationship is what I would call a sophisticated one," he said in reference to Irish and British relations.
Taoiseach Leo Varadkar said that neither the taoiseach nor president attended the last coronation in 1953, adding in that respect their attendance at King Charles' coronation demonstrates that the relationship between both countries is "a much better one, a much deeper one, one of neighbours and one of equals".
Mr Varadkar said that King Charles has shown a genuine interest in Ireland, which he believed would be of benefit in terms of the relationship between both countries.
He said that he briefly spoke with the King at Buckingham Palace last night, and King Charles reiterated his desire to visit Ireland and see every county on the island.
No date has been set but the Taoiseach expressed hope that it may happen later this year.
"I think that would be very welcome," he added.
Speaking earlier, Mr Varadkar said: "We have deep political, economic, cultural, and personal links with Britain, which provided a welcome home to so many of our citizens for generations.
"A vibrant British community actively contributes to life in Ireland in so many ways.
"And, of course, there are many people, in the north especially, who are both British and Irish.
"As we mark the coronation of King Charles III, I look forward to further strengthening British-Irish relations and the friendship between our peoples and look forward to welcoming the royal couple to Ireland in due course."
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Speaking after the coronation, Mr Higgins said that the royal family had shown a great interest in Ireland.
He added that a visit by the King to Ireland in the future would be very much welcomed.
Members of Sinn Féin also attended the coronation. In a post on social media, Michelle O'Neill said that she was attending the event as First Minister Designate of Northern Ireland.
She said: "Today I will attend the Coronation of King Charles III as First Minister Designate. My determination is to keep moving forward, and to represent the whole community. The political landscape across our island is changing. My focus is on building a shared future for all."
