Ulster Unionist leader Steve Aiken has welcomed the Taoiseach's comments that calls for a border poll are divisive.
Speaking in the Dail, Micheal Martin said he didn't believe that "precipitating or organising a referendum like that is the way to go". The Taoiseach added that he favoured stronger North-South relations.
Mr Aiken said: "It's good to see the new Taoiseach appreciating the reality of the situation rather than chasing the destabilising influences of a border poll. I would much rather that we rebuild relationships. We have always said that we want North-South, East-West relationships to work and we want to move away from the toxic relationships of the past. We should seek to use this as an opportunity to improve on what went before."
But Sinn Fein accused the Taoiseach of "abdicating his responsibility as head of government".
Donegal TD Padraig Mac Lochlainn said: "Whilst Fianna Fail occasionally pays lip service to its republican roots, it has long since abandoned any desire to advocate for a united Ireland, particularly under Micheal Martin's leadership.
"A referendum on Irish unity is expressly provided for in the Good Friday Agreement - despite what the Taoiseach thinks. This is an agreement endorsed by the people of this island, north and south, overwhelmingly over 20 years ago."
But SDLP leader Colum Eastwood said: "Micheal Martin is right - no amount of slogans will win the campaign for Irish unity. A successful campaign demands that we build new relationships between the people of this island, maximising North-South cooperation and building on the potential of the Good Friday Agreement.
"It's up to this generation of political leaders to spill our sweat breaking down the decades of mistrust that have divided people and pushed us further apart."
DUP MLA Christopher Stalford said: "We want to be good neighbours with the Republic of Ireland, but being part of the world's fifth largest economy is of direct benefit to people's lives.
"What Northern Ireland needs is not a repeat of tired calls for a border poll, but a fresh desire to actually get on with governing responsibly on behalf of everyone. Republicans have a responsibility to look beyond their own narrow base and work for the greater good of society."