Arlene Foster has sought to reassure people that Northern Ireland and the Republic of Ireland will remain “neighbours” after Brexit.
Speaking on Irish national broadcaster RTÉ, the first minister said she “wanted to send out a message”.
The moment of the UK’s departure from the EU, which happened at 23:00 GMT on Friday, was marked by both celebrations and anti-Brexit protests.
There are no immediate changes as the UK enters a transition period.
On Friday night Mrs Foster told The Late Late Show she wanted people on the island of Ireland to know that “we are and will continue to remain neighbours”.
“Whilst we are leaving the institutions of the European Union, we are not leaving Europe and we are certainly not leaving the island of Ireland,” said the Democratic Unionist Party (DUP) leader.
“We will continue to have those neighbourly relationships.”
Moments after Brexit, Deputy First Minister Michelle O’Neill – the Sinn Féin vice-president – said there was a “momentum of change” towards a united Ireland.
Next week the first and deputy first ministers will chair the first meeting of the Northern Ireland Executive’s sub-committee on Brexit.
While events were held in Northern Ireland to celebrate Brexit, the day was also marked by anti-Brexit protests in Irish border areas.
Mrs Foster acknowledged there were many people who were “scared” about Brexit.
“The first thing to do is not to be triumphalist and acknowledge that some people don’t want it to happen,” said Mrs Foster.
She said while she was pleased about the UK’s exit she was concerned Northern Ireland was “not leaving on the same terms as the rest of the UK”.
Tánaiste Simon Coveney said history was “changing course” as a result of Brexit.
Mrs Foster was also pressed for her views about the prospect of a united Ireland.
“I do not think it will become a reality,” she said.
“There are many reasons why we will stay in the UK – economic, social, political, cultural, our NHS, which we’re very proud of and which needs a lot of work.
“I would be absolutely devastated if I was leaving the UK because I’m a unionist – economically I believe it’s the right thing to do.”
Symbolic appearance by Foster on Irish TV
Analysis: Jayne McCormack, BBC News NI political reporter
Make no mistake – this was a very deliberate decision by the DUP leader to appear on the Irish national broadcaster during the exact moment Brexit happened.
The relationship between Northern Ireland and its closest neighbour came under big strain during the Brexit negotiations.
Many people in Northern Ireland view themselves as Irish and as members of the EU and are concerned about what Brexit means for Irish identity.
The newly-installed first minister was seeking to reassure people on both sides of the border that while there will be some big changes coming in terms of trade, politically now is the time for making up.