The Democratic Unionist leader said in a speech on Brexit in Killarney that the party did not want see the “creation of hard border of the island of Ireland.”
Arlene Foster told the Killarney Economic Conference: “We cannot countenance anything which potentially creates a border down the Irish Sea.
“We absolutely don’t want to see the creation of a hard border in the island of Ireland.”
Mrs Foster admitted Brexit has thrown up some taxing problems over the issue of the Irish border that would “require some novel solutions,” adding “we must accept the reality of the European Union referendum.”
DUP leader Arlene Foster (L) and Prime Minister Theresa May
She said: “We are under no illusion how difficult and complex discussion will be over the coming months.”
She said: “I often think that Northern Ireland and the Republic of Ireland are like a semi-detached house.
“The houses may look the same on the outside, but, inside, they look different and we do many things very differently.
“But no matter how contrasting the interiors are, they are tied together and part of the same neighbourhood and what happens on one side of the fence inevitably has an impact on the other.
“I know that we are rivals in some respects, but in so many ways success for one of us is success for the other.
“As we chart a new course for the future, it is not in our interests to see the Republic of Ireland do anything other than prosper.
“Nor does it help any of us if we let the challenges that Brexit brings deflect us from the opportunities that will exist in the future.
“We will continue to have our own identities and for our part we will no longer be members of the European Union, but our futures will still be closely connected.”
Mrs Foster said: “The Democratic Unionist Party supported the UK leaving the European Union but in so doing Brexit is not about pulling up the drawbridge, building a wall and cutting ourselves off from our nearest neighbours.
Prime Minister Theresa May on the local election campaign trail
“But we must all recognise that change is coming as a result of the referendum.
“It is our job as politicians to help shape that change but to do so in a way that ensures that those economic, cultural and social ties that have endured through difficult times and have thrived through better ones continue into the future.
“We want to avoid a cliff edge for businesses by having a strictly time limited implementation period.”
The DUP chief said she planned to raise the prospect of enhancing Anglo-Irish relations, under the auspices of the British-Irish Council, when she meets Ireland’s Foreign Affairs Minister Simon Coveney.
She said: ”Maintaining Northern Ireland’s economic and political status as an integral part of the United Kingdom is absolutely crucial to me and my party.”
DUP leader Arlene Foster, with party colleagues Simon Hamilton and Edwin Poots
“To think anything else would be as foolish as believing that the Taoiseach – Leo Varadkar – or the Tanaiste – Mr Coveney – desired anything other than Irish unity.
“But while we will always battle for our own national interests, we must also battle for our mutual interests.
“And our mutual interests will not end on the day the UK formally leaves the European Union. The United Kingdom may be leaving the EU but the common interests that we share across the British Isles will remain.”
The DUP suggested Anglo-Irish relations could be deepened through the British-Irish Council, which was set up as part the Good Friday Agreement to improve co-operation between the UK and Ireland in areas such as transport, the environment and energy.
“The UK exiting the European Union ought not to become a barrier to continued co-operation on issues of ongoing mutual interest,” she said.
“It especially shouldn’t become a barrier when the infrastructure – in the guise of the British-Irish Council – already exists that can allow us to continue to work together as closely as ever on issues of shared interest.”
Mrs Foster gave the example of the Nordic Council, which includes Denmark, Finland, Iceland, Norway, Sweden, the Faroe Islands, Greenland and Aland as a means for developing Anglo-Irish relations. She noted that some of the Nordic countries are in the European Union and Eurozone, while others are not.
“Change should not be allowed to weaken the relationships so painstakingly put together across these British Isles,” the DUP leader said.
“As challenging as finding a suitable solution might seem, there is no good reason why our own issues on this island should present any threat to the progress we’ve made.
“I value the relationships we have developed too much to do anything that would jeopardise them.
“But, whether we voted to leave or voted to remain, whether we are citizens of the United Kingdom or citizens of Ireland, we must accept the reality of the referendum result, refrain from the continued re-fighting of the referendum, and seek the sensible, mutually beneficial outcomes from the complex negotiation process ahead that will serve us all well.”