First Minister Arlene Foster has said she is not threatened by a new shared island unit established by Taoiseach Micheál Martin.
If a border poll was called, people in Northern Ireland would vote to remain in the UK, the DUP leader added.
Mr Martin has said a referendum on a united Ireland would be too divisive but favours development of a stronger north-south relationship.
On Friday, 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.
Just finished a very constructive briefing with the PM @BorisJohnson relating to covid-19 challenges across the UK.— Arlene Foster #We’llMeetAgain (@DUPleader) July 31, 2020
Welsh & Scottish counterparts also part of the call.
Key sectors in our economy still need support and we all must stay alert to curb any second waves.
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 pandemic.
“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.”
Very positive and open discussions at today’s North South Ministerial Council. I’m looking forward to an ongoing focus and continuing engagement so that together we can address the challenges facing people on our island pic.twitter.com/GoQNyImaaT— Micheál Martin (@MichealMartinTD) July 31, 2020
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 powersharing pledged to “turbo-charge” connections between Dublin and Belfast.
The Government also promised to jointly fund cross-border investment on bridges, roads and canals.
The 24th plenary meeting of the North South Ministerial Council (NSMC) was held at Dublin Castle on Friday – the first since before the collapse of Stormont powersharing.