Taoiseach Leo Varadkar today held a "constructive and warm meeting" with Scottish First Minister Nicola Sturgeon at Government Buildings, according to a statement released by the Government.
Mr Varadkar and Ms Sturgeon discussed a number of issues, primarily the ongoing challenge of Brexit and the political situation in the UK and Northern Ireland.
Both expressed a desire that the UK should remain in the single market and the customs union, as well as a desire that the institutions in Northern Ireland be restored at the earliest possible opportunity.
The Scottish Executive and Ireland already enjoy close relations in the areas of business, and culture and both leaders "pledged to develop ever closer bilateral relations".
Mr Varadkar has also accepted the First Minister's invitation to visit Scotland.
Both he and Ms Sturgeon will meet again in Jersey at the next meeting of the British Irish Council in November.
Following the meeting Ms Sturgeon spoke in front of an audience of business leaders in Dublin where she declared that Ireland and Scotland are allies in the Brexit negotiations.
The Scottish First Minister said that she will argue for the Irish border to remain open in the wake of the UK's split from Europe.
She also said that Mr Varadkar and her are united on virtually every issue of substance relating to Brexit.
Ms Sturgeon told an audience of about 1,500 business figures that staying in the European single market and the customs union is the obvious answer to the negotiations.
"The fact that the UK Government is committed to leaving the EU means that Scotland - like Ireland, and like Northern Ireland - now faces a dilemma which is not of our choosing. We want to remain a full member of the EU but face being taken out against our will," she said.
"We deeply regret that.
"However, we believe that if the UK is determined to leave the European Union, it should remain a member of the single market and the customs union.
"In my view, that is the obvious compromise solution. It's democratically justified - the vote to leave was a very narrow one across the UK and two of the four nations of the UK chose to remain."
In her speech to the Dublin Chamber, she also disputed British Prime Minister Theresa May's recent remarks in Florence and claimed that in Scotland many people have felt absolutely at home in Europe.
She also emphasised the social and economic links between Scotland and Ireland, and noted the shared interest in ensuring the growth of a global economy is matched by a focus on inclusion.
Ms Sturgeon said leaving the single market will be deeply damaging for Scotland's businesses, universities, trade and jobs.
"On virtually every issue of substance relating to Brexit, the Irish Government - and the Irish business community as a whole - has an ally in Scotland," the First Minister said.
"Like you, we didn't want Brexit.
"Like you, we support single market and customs union membership.
"And, like you, we know that Ireland's circumstances require particular attention and we will argue strongly for an open border.
"We believe that those positions are in the best interests of Scotland, of Ireland, and of everybody on these islands."
Ms Sturgeon told business figures the global political developments are a challenge to build a fair and inclusive society.
She added: "Scotland certainly hasn't got everything right, but - like Ireland - I think that we are at least facing up to the right issues.
"That's important from a political, social and moral perspective - and it's also crucial to ensuring that our economic policies are successful and sustainable."