Democratic Unionist leader Arlene Foster, who campaigned for an EU exit, said she was “absolutely certain” the constitutional status was secure and claimed the union was stronger after the Leave vote.
Her comments come after Sinn Féin, the DUP’s partners in the power-sharing government, said the result of the referendum should trigger a border poll.
In Northern Ireland 440,707 (56%) people voted to Remain and 349,442 (44%) to Leave. Of the region’s 18 constituencies, 11 voted Remain and seven voted Leave.
A border poll can only be called by the region’s secretary of state in circumstances where there is clear evidence of a public opinion swing towards Irish unity.
Northern Ireland secretary Theresa Villiers said she did not believe the criteria for triggering a border poll had been met.
Ms Foster rejected the Sinn Féin demand, saying: “The call for a border poll was as predictable as the flowers in May.
“We knew it would come but the test has not been met so therefore I don’t believe it will happen.”
The DUP leader added: “I think we are now entering a new era of an even stronger United Kingdom.
“I am very much looking forward to working with our colleagues in our national government to build a very strong, outward-looking UK moving forward and of course Northern Ireland as a very key constituent part of that.”
The renewed focus on Northern Ireland’s constitutional position comes as Scotland’s first minister Nicola Sturgeon said a second referendum on Scottish independence was “highly likely”.
Stormont deputy first minister Martin McGuinness said the people of Northern Ireland must have a say on their own future.
The Sinn Féin veteran said the region is in “unchartered waters” and he would seek “urgent” talks with the Irish and Scottish governments and EU institutions on “how we move forward in the best interests of all of our people”.
Taoiseach Enda Kenny said there was no evidence of a shift in the Northern Ireland electorate for a border poll on a united Ireland.
“That [provision for a border poll] is contained in the Good Friday Agreement, provided that the secretary of state of the day considers that there would be a serious movement of a majority of people to want to have a situation where they would join the Republic,” he said.
“There is no such evidence.”