The Irish premier has ruled out a border poll as “far too divisive at this stage”.
Micheal Martin said he instead wants to focus on building relationships to share the island of Ireland “in peace and harmony”.
He also urged an “injection of momentum” in the Brexit talks between the UK and EU to find a deal to secure a deal before the end of the transition period.
Sinn Fein has been calling for a border poll amid the political turbulence caused by Brexit and uncertainty over future arrangements.
Mr Martin’s new coalition government includes an all-island unit in the Department of the Taoiseach “to develop fresh thinking around that”.
“I want to inject greater momentum into the north-south dimension of the Good Friday Agreement, in terms of practical, pragmatic economic projects and activity that we can get under way,” he told the BBC’s Andrew Marr Show.
“I think, to me, a border poll is far too divisive at this stage, it doesn’t deal with the more fundamental issue of how we continue to live and work together as we all live on this island, particularly in a post-Brexit scenario.”
The Taoiseach is due to visit Northern Ireland for his first time as Irish premier later this week.
First Minister Arlene Foster told the Sunday Politics programme that she and Deputy First Minister Michelle O’Neill will meet Mr Martin jointly.
The pair have not appeared together since the row over Ms O’Neill’s attendance among huge crowds at the funeral of veteran republican Bobby Storey in west Belfast on 30th June.
Police are probing that event for potential breaches of coronavirus regulations.
Mrs Foster said: “We will welcome him to Northern Ireland to have discussions, respecting jurisdictions, making sure that we look forward to the future in a way that doesn’t do any damage to the relationships which have come under pressure in over the last couple of years.”
She reiterated her belief that the message on social distancing has been damaged by Ms O’Neill’s actions, but added: “It is now up to us all to try and rebuild that credibility…it’s important we don’t get distracted by looking at who is standing beside who but actually do the job of work of government, providing leadership.”
Mrs Foster said she will not “prejudge” the Taoiseach but will wait to see his actions.
Mr Martin said he understood the wish to attend a friend’s funeral but added that everyone is subject to the coronavirus restrictions.
“I understand the frustration of people who witnessed the large turnout at that funeral, but, as co-guarantor of the Good Friday Agreement, my overall perspective on this is to try to ensure that this doesn’t damage or undermine the institutions in the north; we have had a long period without the Northern Ireland Executive or the Assembly,” he said.
Meanwhile, Mr Martin also said more detail is needed on arrangements following Brexit, and expressed concern about the “significant divergences” remaining between the EU and the UK on a post-Brexit trade agreement.
“I think there has been some progress in terms of a paper that the UK Government published, but we do need more detail, we need more precision.
“I think we need an injection of momentum into the overall talks between the European Union and the United Kingdom in relation to Brexit,” he said.
“I had a very fruitful discussion with the Prime Minister, Boris Johnson, after I took office. I think we both agreed that it’s in everybody’s interest, particularly in terms of businesses and giving them certainty, that we get a good comprehensive trade deal between the UK and European Union.
“Our concern is time is tight in relation to all of the mechanisms that have to be gone through in terms of getting the sanction and the approval of the EU member states and the European Parliament and our respective governments.”
The Taoiseach said he believes the European Court of Justice is just one of “a number of sticking points” in discussions.
Picture: File photo, dated 6th June 2020, shows Taoiseach Micheal Martin who has ruled out a border poll as “far too divisive at this stage”. Sinn Fein has been calling for a border poll amid the political turbulence caused by Brexit and uncertainty over future arrangements. (Niall Carson/PA).