The Irish prime minister, Leo Varadkar, has said he does not want an economic border between Britain and Ireland.
He was speaking at Queen's University, Belfast, on the future of north-south relations, during his first official visit to Northern Ireland.
In the afternoon, he will hold meetings with political parties.
The taoiseach warned that those who want a hard Brexit must come up with a plan to deal with the border.
On Saturday, Mr Varadkar, who is the Republic of Ireland's first openly gay taoiseach, will attend an event as part of Belfast's gay pride festival.
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Mr Varadkar said: "It will come as no surprise to anyone here that I do not want there to be an economic border on our island, nor do I want one between Ireland and Britain.
"By economic border, I am not talking about currency or variation in tax rates. I am talking about a barrier to free trade and commerce."
Mr Varadar also urged politicians to do a deal to restore power-sharing in Northern Ireland.
The taoiseach is to meet the DUP, Sinn Féin, the SDLP and the Alliance Party later on Friday. He will not be meeting the Ulster Unionist Party as its leadership was not available.
Analysis: Enda McClafferty, BBC News NI political correspondent
Leo Varadkar has already ensured his first trip over the border as taoiseach will be one to remember.
His decision to attend the gay pride breakfast gathering as the Republic's first openly gay Taoiseach is sure to grab the headlines on Saturday.
But, it will be his speech at Queen's University and his meeting with the DUP, in particular, that will be the main focus on Friday.
That's because the DUP this week accused the taoiseach of engaging in "megaphone diplomacy" and being unhelpful when he suggested Brexit supporters should be the ones to design a new border.
His meeting with DUP leader Arlene Foster will come days after a row between the party and the taoiseach over the Irish border post-Brexit.
Mr Varadkar had said he would not design a border for Brexiteers but DUP MP Jeffrey Donaldson said that "megaphone diplomacy from Dublin" would not sort out the border issue.
Speaking on Good Morning Ulster on Friday, Sir Jeffrey said his party welcomed the opportunity to sit down with the taoiseach.
"It is better to have dialogue than what we've seen in recent weeks which is the Irish government making statements about a border in the Irish Sea which is totally impractical and a non starter," he said.
"We have to negotiate our way through this.
"We want a comprehensive free trade and customs agreement, we want a common travel area. These are the objectives we've set, we're negotiating with Brussels, but Dublin is currently disengaged."
On the same programme, Sinn Féin MLA Conor Murphy said the taoiseach was "acting in the interests of the people of Ireland when he makes these remarks and these approaches to the European Union".
"If they (the DUP) want to see a new arrangement which effectively is the same as the old, why leave the European Union?" Mr Murphy continued.
"We have to ensure that our interests are up there. The fact that we are Irish citizens and European citizens and we have rights to be protected, needs to be front and centre. And we look to the taoiseach to defend our interests."
On Thursday, former taoiseach John Bruton, who was also a former leader of Mr Varadkar's Fine Gael party, said that the DUP is in a position to answer questions over Brexit because of its Westminster pact with the Conservative Party.
"Do they (the UK government) want to leave the customs union? Are they willing to accept being in the European Economic Area? What type of agriculture policy will the UK government pursue post-Brexit?
"These are all questions that Arlene Foster is in a position to answer because she's critical to the continuance of the current UK government."