First Minister Arlene Foster has said she is not threatened by a new shared island unit established by Taoiseach Micheal Martin.
The DUP leader said she was confident that if a border poll was called, people in Northern Ireland would vote to remain in the UK.
Mr Martin has said a referendum on a united Ireland would be too divisive but favours development of a stronger north-south relationship.
Yesterday he said progress had been made in discussions on better rail links between Belfast, Dublin and Cork, and the building of a greenway cycle route between Sligo and Enniskillen in Co Fermanagh.
The leaders were gathered for a meeting of the North South Ministerial Council at Dublin Castle yesterday.
Mrs Foster said: "We do share an island and there are two jurisdictions on the island and I will never shy away from speaking about my unionism and why I believe in the union."
She added: "There is nothing to fear from having these discussions about the island."
She said it does not change what she believes in but it is always good to talk and share information, as they have done throughout the Covid-19 pandemic.
"It does not threaten our constitutional position or what we believe in so I don't feel threatened at all by the shared island unit," Mrs Foster added.
"I have to say everyone knows my position in relation to a border poll.
"If it was called today, of course people would vote to remain in the United Kingdom, although I'm sure Michelle (Deputy First Minister Michelle O'Neill) would take a different view, therefore I have nothing to fear from that."
Mr Martin previously said an all-island unit to be established in his department would be focused on how to develop a shared future.
January's New Decade, New Approach deal to restore Stormont power-sharing pledged to "turbo-charge" connections between Dublin and Belfast.
The Dublin Government also promised to jointly fund cross-border investment on bridges, roads and canals.
Yesterday's event was the 24th plenary meeting of the North South Ministerial Council - and the first since before the collapse of Stormont power-sharing.
At the meeting, the Deputy First Minister warned that time is running out in relation to Brexit.
Michelle O'Neill said that people in Northern Ireland have been left in the dark over the outcome will be. She called for "certainty and clarity" and for the protocol to be fully implemented. She added: "Time is running out. We are at the 11th hour and now have about four months left before we get to the end of the year.
"We have a situation where citizens in the north are still not sure what the outcome will be so we need certainty and clarity.
"For us, we have to have the protocol implemented in full as that gives us our protection and recognises our special and unique circumstances on this island in terms of protecting the trade and having no hard border on the island."
Mrs Foster said that businesses and people in Northern Ireland should not face any barriers when doing trade with Great Britain.