There have been tensions between the two leaders
The Taoiseach Enda Kenny has met with Northern Ireland's First Minister Arlene Foster at Government Buildings to discuss the implications of Brexit.
There have been tensions between the two leaders, after the DUP leader refused to attend Mr Kenny's all-island forum on Brexit.
Meanwhile, Ms Foster has denied suggesting at her party conference that the republic was trying to "poach" investment from the North.
Speaking before the meeting, she said the talks would be business-like.
Meanwhile a UK Supreme Court judge has suggested a British exit from the European Union could be delayed by months, even as long as two years.
Justice Brenda Hale suggested that "comprehensive" legislation was required to trigger Article 50.
She told an audience in Kuala Lumpur that the court must question "whether it would be enough for a simple act of Parliament to authorise the government to give notice, or whether it would have to be a comprehensive replacement for the 1972 [EEC Accession] Act".
Britain's Supreme Court will begin hearing a case on December 5th, after a UK High Court ruling that the Prime Minister Theresa May cannot trigger Brexit without putting it to a vote in the House of Commons.