Taoiseach Micheál Martin has said he does "not see the possibility" of a border poll taking place during the lifetime of the new Government.
"But what I would like to see is significant work under way as to what a shared island would look like.
"I grew up in a tradition that wanted a united Ireland. The Good Friday Agreement was a fantastic breakthrough - yes it does have a provision for a border poll but also for the principle of consent."
Speaking on RTÉ's Six One News during his visit to Northern Ireland today, Mr Martin said one of the last conversations he had with the late Seamus Mallon has stayed with him.
"He told me 'people have been living in this location for 400 years, it's about time we learnt how to share it'. His thinking has influenced me."
Mr Martin added: "We could have a border poll in the morning, it could lose, it could win, but does it move things forward in areas such as health, education, business? I am not so sure it does."
He also said he had talked to British Prime Minister Boris Johnson about a trade deal on Brexit.
The Taoiseach said a 'no deal' Brexit would cause economic havoc and it would take "political will" to make sure that did not happen.
A busy day. Constructive discussion with new Taoiseach Micheál Martin. We want to have a good neighbourly relationship based on mutual respect.— Arlene Foster #We'llMeetAgain (@DUPleader) July 16, 2020
Just finished a useful Joint Ministerial Committee meeting involving HMG alongside the devolved govts in Scotland, Wales and NI.
Micheál Martin made it crystal clear that Northern Ireland and North-South relations are going to be a critical part of his Government's policy.
He vowed to get key North-South infrastructure projects "over the line" after his meeting at Stormont Castle with First Minister Arlene Foster, Deputy First Minister Michelle O'Neill and Britain's Northern Ireland Secretary Brandon Lewis.
The North South Ministerial Council of ministers from Northern Ireland and the Republic will meet at Dublin Castle on 31 July for the first time in three and a half years.
I welcome today's visit by An Taoiseach @MichealMartinTD for a Heads of Government meeting with Arlene Foster and I. We discussed a range of issues including the all-island Covid response and our economic recovery & Brexit. We look forward to a full NSMC on 31 July in Dublin.— Michelle O’Neill (@moneillsf) July 16, 2020
Mr Martin also promised his Government would help jointly fund cross-border investment on bridges, roads and canals.
He told a press briefing: "I will be an engaging, understanding Taoiseach, trying to keep people together and trying to move forward on the economic front in particular and also in terms of getting projects over the line that we have been talking about for some time."
Mr Martin said the 1998 Good Friday Agreement which enshrined the devolved institutions at Stormont and cross-border bodies was his "touchstone".
He promised to take a pragmatic approach based on nurturing key relationships underpinning peace and reconciliation on the island.
The Taoiseach said he understood the need to build relations and had met with loyalists and unionists in the past.
Mr Martin said he had a "very good series of meetings" today with Ms Foster, Ms O'Neill, Mr Lewis and other political leaders in Northern Ireland.
He said there was a "genuine desire on all sides to work together".
Micheál Martin says he understands the necessity of building relationships in politics, and his approach regarding North-South relations will be a 'pragmatic' one. | Read: https://t.co/GPPCps7MVX pic.twitter.com/yosDpWqsZh— RTÉ News (@rtenews) July 16, 2020
Asked about the Government's shared island unit, the Fianna Fáil leader said the unit would work without prejudice to people's political positions.
Mr Martin told reporters he felt a border poll would be too divisive and he would prefer to explore "the economic, social and political issues that would enable us to share the island in a peaceful way".
Watch: Taoiseach Micheál Martin speaks to RTÉ's Northern Editor Tommie Gorman on Barry Cowen's dismissal, his problems in Fianna Fáil, the Covid challenge, North-South relations, the possibility of a Brexit deal, and why there won't be a border poll.
First Minister Arlene Foster said: "We had a productive discussion around areas of mutual interest. Recovery from the coronavirus pandemic was a key focus of our conversation as we work simultaneously to protect people and rebuild our economies.
"As two jurisdictions sharing an island it makes perfect sense that Northern Ireland seeks to build a positive relationship with our neighbours in the Republic of Ireland.
"We have seen the benefits of collaboration through the North West Cancer Centre and the all-island Congenital Heart Disease Network, for example."
Deputy First Minister Michelle O'Neill said: "We discussed economic recovery from the Covid-19 pandemic as well as the ongoing public health response and the need for a joined up approach across the island where possible.
"We spoke about the potential implications of Brexit and the pressing concerns this raises. I set out the need to work together to protect the needs and interests of people and businesses across this island."
UUP leader Steve Aiken said: "We would like to go back and reset the relationship to three years ago where we had a respectful dialogue between north and south, between the Taoiseach and leader of the Ulster Unionists and various other parties.
"With this Taoiseach we have probably got the opportunity to do that."