First Minister Arlene Foster has not talked to the Taoiseach Micheal Martin "in quite some time".
Mrs Foster, in a wide ranging interview with RTE's departing Northern Ireland editor, Tommie Gorman, also said the Northern Ireland Protocol has harmed the region in different ways.
"I think we have seen the real and meaningful way it has damaged commerce in Northern Ireland," said Ms Foster.
"Then moving away from the economy piece, which is hugely important, have to deal with the identify piece."
But the bigger picture is about identity, she said, arguing that some people are not listening when the unionist and loyalist communities say they are part of the United Kingdom.
"It's dangerous when people think they are not being listened to," Mrs Foster added.
The DUP leader still believes in Brexit, saying that the EU's "behaviour over vaccines" reinforces her thinking, adding she is "very glad" to have voted leave in the referendum.
On a united Ireland, the Fermanagh MLA believes there is no argument.
She said: "Anybody, objectively and rationally where we are in Northern Ireland - look at the National Health Service, look at our vaccine roll out, look at our financial wherewithal.
"Thanks to the intervention of Whitehall, why would anybody want to move away from that, rationally and objectively?
"There is no argument for a united Ireland."
The fundamental position for unionists is they want to remain in the United Kingdom, she said in the interview, broadcast yesterday on RTE.
"It's much more fundamental than just saying you can keep your Twelfth of July or change the name of the Prime Minister or Deputy Prime Minister, that is not what unionism is about."
Ms Foster envisages a future Northern Ireland at peace with itself, and everyone respecting differences, within the UK.
But if there was a vote in favour of a united Ireland, the DUP leader said she would leave her home.
"Because I do not think I would feel comfortable and that is why I would leave... because what's the point in staying in a place where I do not feel comfortable and where your identity would not be something that would be respected?
"I cannot see how I could be British in Fermanagh, in a united Ireland, because by the very definition, you are no longer British because you are living in an all-Ireland state."
In response to questions about whether the UK should share its vaccines with the Republic of Ireland, Mrs Foster said: "I have not been talking to Micheal Martin for quite some time now," adding that she believes sending vaccine supplies across the border is the right, and practical, thing to do.
"It should happen and hopefully it will," she told the Week in Politics.
Deputy First Minister Michelle O'Neill, also interviewed by RTE, said she and Ms Foster had much in common, as female leaders, mothers and both hailing from west of the Bann.
The two "agree to disagree well", Ms O'Neill said, adding that the Northern Ireland Protocol - which has created a post Brexit trade barrier between Northern Ireland and Great Britain and is opposed by unionists - is not up for renegotiation.
"It's not about myself against Arlene Foster, it's not about Sinn Fein against DUP, it's about the fact the DUP and political unionism... hitched their wagon to the Tories and the Tories have time and time again reneged on the promises made," Ms O'Neill said.
"It's far from perfect, it has many faults and failings... however it does give us some protections in terms of the all-Ireland economy with no hard border on the island."
On a potential border poll, the Sinn Fein MLA said her party is focusing on planning for the future, including what the health service, education and the economy will look like on the island, and the north-south, east-west relationships.
"We have all been victims of partition, not just republicans and nationalists, unionists included, everybody who lives on this island has been the victim of partition and I think there is a chance of doing something better, and make sure the new generations do not fight the battles of the past."
Ms O'Neill said she hopes Mrs Foster will rethink her position on leaving Northern Ireland if the island is ever united.
"The new Ireland that we foresee has to be something for us all; it's not for nationalists or republicans, (it) has to be that allows for those with a British identity to live side by side," she said.
"There's something huge that for us all that we can walk through the door together."