Britain’s Prince Charles has held private, separate meetings this evening with Fianna Fáil leader Micheál Martin and Sinn Féin leader Mary Lou McDonald.
Both meetings lasted more than half an hour.
It is understood Prince Charles listened to Mr Martin's observations on the current situation in Northern Ireland and on British-Irish relations post-Brexit.
The Prince of Wales also expressed a desire to attend a hurling match during a future visit.
After her meeting, Ms McDonald said she was glad to avail of the opportunity to extend the hand of friendship not just to the Prince of Wales but also to those in Ireland who identify as British.
Prince Charles and his wife Camilla were in Cork today for a round of engagements, which included a visit to the city's English Market.
The couple started by following in the footsteps of Britain's Queen Elizabeth II and travelling to the city's famous English Market.
It follows a two-day visit to Northern Ireland, ending yesterday in Omagh, where they paid their respects at the scene of one of the biggest mass killings of the Troubles.
There was a party atmosphere in Cork as the royal visitors were greeted by a local band - the product of a nationwide music education programme initially part-funded by the rock stars U2 - playing pop hits for hundreds of schoolchildren gathered outside the market and crowds lining crash barriers.
Tánaiste Simon Coveney welcomed the visit saying: "Royal visits enforce the normalisation of a confident and independent Ireland today with its closest neighbour, and the fact that we've moved on from the hang-ups of the past.
"Prince Charles has been to the island three times in the last three years. Today he's seeing the best part of Ireland and I think he'll get a very warm reception here.
"As you can see, people of all ages are here to make sure this is a positive day for Cork."
Cork's food hall is named after the English corporation that established the centre in the 18th century and this year the tourist attraction celebrates its 230th anniversary.
It first began trading meat in 1788 but fish, vegetables, fruit and other goods were later added.
Today it serves all markets, from those wanting the latest trends in cuisine to locals buying traditional fare such as tripe or blood pudding known as drisheen.
The prince and duchess went on a brief walkabout after they stepped from their motorcade, meeting some of the enthusiastic schoolchildren.
Soon after arriving inside the market, the couple cut a 230th birthday cake to mark the milestone of the foodhall the Queen toured during her historic 2011 visit to Ireland.
Nearby, they were immortalised in icing with their faces decorating a display of cup cakes.
The couple were hosted by Lord Mayor Councillor Tony Fitzgerald at a civic reception at Cork City Hall at noon.
Seventy-two seconds of silence was observed for the 72 victims of the Grenfell Tower blaze during the reception marking the first anniversary of the devastating fire.
The prince addressed Cork City Hall in Irish before he began his speech. He said: "You have no idea what a joy it is for me and my wife to be back in Ireland again.
"Your kindness in letting us return is deeply appreciated. "We have been profoundly touched by the warmth of the reception we have received. We have felt every single one of the 'céad míle fáiltes' extended to us.
"Ireland is a country that my wife and I have come to love. Above all, the warmth of its people and the irresistible haunting beauty of its landscape"
The prince was cheered by students when he arrived for a tour of University College Cork. He was greeted by the institution's President Professor Patrick O'Shea.
During his visit to the university, he was shown inside a recreated famine hut, to illustrate rudimentary living conditions facing many during the mid 19th-century shortages.
He was also introduced to several high-achieving students.
Among them was disability activist Joanne O'Riordan, 22, a fourth-year criminology student. She previously addressed the UN on disability rights issues.
The prince was also shown a manuscript containing handwritten entries by some of Ireland's greatest literary figures, including the last written words of Samuel Beckett.
A harpist entertained the prince before he signed a visitor book. Among those he met are beekeepers, who are using the latest technology and in-hive sensors to increase productivity.
The Duchess of Cornwall visited a women's refuge in Cork city for victims of domestic violence. The centre, which has served the area for more than 40 years, offers counselling and support for women and children.
She hailed the work of the refuge for letting women know "they are not alone".
She presented a hamper to the refuge filled with sweets, chocolate and fudge for the children who live there, and met the artist in residence who works with children through art therapy.
The mother of a seven-year-old boy who presented the Duchess of Cornwall with a card in Braille says she was "delighted" after the private secretary to the duchess told her it was the first card she had received of its kind.
At the National Maritime College and the Naval Service Headquarters, Prince Charles boarded the LÉ William Butler Yeats, the newest ship in the Navy's fleet of offshore patrol vessels.
He met some of the families of crews currently on rescue missions in the Mediterranean.
The ship embarked on a three-month deployment in the Mediterranean last year during an intensive period of the ongoing European migrant crisis.
The couple will spend tomorrow in Co Kerry.
Additional reporting Paschal Sheehy and Teresa Mannion