DUP MP Gregory Campbell has told President Catherine Connolly "you're in our country" and warned her against "rewriting the past" on her visit to Co Derry.
In a short interaction between the pair after President Connolly addressed the Guildhall, she said she is "here to listen" - adding "at the end of the day we're human beings and we have to have respect".
Referring to his attendance this evening at a debate in Dublin, the DUP MP told the President: "You're in our country. Tonight I'm going to your country."
He added: "We're not leaving the United Kingdom, not now or at anytime in the future, so I think it's better if we try and ensure no-one rewrites the past as we all build for the future."
Mr Campbell said he wanted to "make our acquaintance to try and build on that".
President Connolly replied: "We're here to listen and to learn from each other and rewriting history would be..." when Mr Campbell interjected "a big mistake", to which Ms Connolly agreed, saying: "In any country and in many countries they've rewritten history to suit a narrative."
Mr Campbell added: "As you said yesterday, it would be a dull day if we agreed on everything - so there's going to be issues where we disagree."
President Connolly told Mr Campbell she grew up in a family of 14 and there were "lots of disagreements, but we had to learn to live and love, at the end of the day we're human beings and we have to have respect, that's very important".
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Speaking to reporters after the meeting, the unionist politician said he "warmly welcomed her to this part of the United Kingdom" and he "always welcomes visitors, especially visitors from other countries".
"I was more than disappointed that in her speech there were numerous references to Derry, but not a single reference to Londonderry," Mr Campbell said.
'The path from conflict to peace'
President Connolly praised the resilience of the people of Derry and their part in the peace process.
Addressing guests at a civic reception in the city's Guildhall, she praised former SDLP leader John Hume, Ulster Unionist leader David Trimble and Sinn Féin leader Martin McGuinness for their contributions.
"Derry has shown us the path from conflict to peace, from its pivotal role in the Northern Ireland Civil Rights Movement, to the Good Friday Agreement, to the ongoing work in the community," she said.
"We remain indebted to your very own, the late John Hume, whose Nobel Peace Prize is displayed here, the late David Trimble with whom he shared that prize, the late Martin McGuinness, and all those women and men who have helped to realise peace.
"In this journey from conflict to peace - a journey that is ongoing - what shines through for me is the resilience, courage, and perseverance of the people of Derry, along with their wit and sense of humour," she said.
During her speech the President referenced the suffering of people around the world.
She said they did not need to suffer because people had voices.
An injustice in Derry was the same as one in Gaza or one in Sudan, she said.
The families of the victims of Bloody Sunday have welcomed a meeting with President Catherine Connolly.
Around 35 family members, representing the dead and injured met the President for around 40 minutes.
The meeting was held in private following a tour of the Free Derry Museum.
It commemorates the struggle for civil rights and the shooting dead of 13 unarmed demonstrators by British soldiers in the city in 1972.
The President was photographed with some of the relatives in front of the civil rights banner carried on the anti-internment march that day.
Tony Doherty, chair of the Bloody Sunday Trust, said families had been pleased she'd taken the time with them.
"It is, I suppose, a sign of maturity as well," he said. "The president's office isn't reticent or afraid to address core issues.
"And for Derry, the core issue of Bloody Sunday is a very, very important one."
Earlier, the President had said she was conscious of recent court decisions and that justice was still awaited in regards to the case.
Last October, Soldier F, a former British paratrooper, who had been on trial for two counts of murder and five of attempted murder linked to the events of Bloody Sunday, was acquitted.
The President is on the second day of a three-day visit to Northern Ireland, the first official visit of her presidency.
She will also today visit the Siege Museum which tells the history of the siege of city in 1689 and the formation of the Apprentice Boys - one of the loyal orders.
Yesterday, President Connolly said the Good Friday Agreement, signed in 1998, stood as an example to a troubled world that peace was possible.
The President's visit to Northern Ireland marks the first official visit of her presidency and fulfils a commitment made in her inauguration address that her first official visit would be to Northern Ireland, where she would meet with people from all communities and celebrate the rich heritage and traditions of all who live there.
She began her official visit with a number of engagements in Belfast, including a meeting with First Minister Michelle O’Neill and Deputy First Minister Emma Little-Pengelly at Stormont Castle, an address at Ulster University, and a number of community engagements.
The visit will conclude with a further engagement in Derry tomorrow.
