The DUP leader has said Brexit is not about pulling up a drawbridge and cutting off Northern Ireland from its nearest neighbours.
Arlene Foster was speaking at the Killarney Economic Conference in Co Kerry.
After the at-times-strained relationship between her party and Dublin during the first phase of the Brexit negotiations, today's speech by Ms Foster struck a conciliatory note.
She said it was in Northern Ireland's best interests to see the Republic of Ireland prosper, and she urged both sides to work not just for their national interests but also for their mutual ones.
The futures of both will still be closely connected and they are underpinned by close economic and cultural ties, she said.
The DUP leader said there had been extraordinarily positive relations between North and South since the Troubles ended and none of this must be lost.
She said the progress made was hard won and that she loses none of her unionism by saying she is proud of that progress.
Ms Foster insisted Brexit was happening, but it is the job of politicians to ensure the close ties between North and South continue and her party does not want to see a hard border on the island of Ireland.
But she said the atmosphere around the next phase of Brexit talks must improve and warned that negotiators must not rush for microphones at the first opportunity.
The DUP is advocating an expanded role for the British Irish Council along the lines of the council that facilitates trade between the Nordic nations.
Ms Foster also held talks with Fianna Fáil leader Micheál Martin at the conference.
Mr Martin, who also addressed the conference, said he sensed a determination from the DUP leader to work towards restoring the Northern Executive.
"The continued absence of an Executive and Assembly is extremely damaging to Northern Ireland in the context of the Brexit negotiations," he said.
Mr Martin agreed with Ms Foster's criticism of "megaphone diplomacy" in the heat of Brexit negotiations.
"We need far more considered discussions and engagements. One always has to respect the position of those you are negotiating with," he said.
"Some of what has gone on has been, in my view, damaging enough in terms of articulating positions too freely in public, to be frank, in advance of negotiations being complete. It's not the way to do business."
Mr Martin added: "I detect from Arlene Foster a clear commitment to the restoration of the Assembly and Executive and a belief that it's the right thing for Northern Ireland.
"In terms of Brexit ... I think the focus needs to be on very practical and constructive engagement to mitigate the damage that in my opinion Brexit will do to trade and jobs between north and south and east and west."
Speaking in response to Ms Foster’s remarks, Sinn Féin’s northern leader Michelle O’Neill said: "I welcome the acknowledgement by Arlene Foster in Killarney today that our economy, community, and future, North and South, are interlinked and interdependent.
"However, this cannot distract from the fact that Brexit will be disastrous for all of Ireland. There is no good Brexit. Today was a difference in tone, but not in policy," said Ms O'Neill.