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Mrs McDonald said a priority for her was that preparations for a border poll should begin and added that those conversations needed to include unionists in Northern Ireland.
Sinn Fein recently topped the poll in the Northern Ireland Assembly elections for the first time, and a number of opinion polls have shown the republican party with a lead among decided voters in the Republic.
Appearing on Sky News’ Sophy Ridge On Sunday programme, Mrs McDonald was asked what was her tipping point for calling for a referendum on Irish unity.
She said: “There will have to be two referendums, in the north and south, in both jurisdictions.
“At this point the big priority for me and for us is that preparation for such a referendum is under way.
“We have to have a very wide, all of society conversation and that has to include unionism, those who will campaign against reunification, those for whom as we move into a united Ireland this will not be their first preference.
“We need to hear all of those voices and so I have urged Dublin to begin the preparation now, I think there is nothing to be gained by burying our heads in the sand.
The recent election in the north is just the latest demonstration of how profound the change is across Ireland
Mary Lou McDonald
“The recent election in the north is just the latest demonstration of how profound the change is across Ireland.”
The Sinn Fein president added: “The Government at Westminster, the British Government, have to indicate what their view is, how they view the matter of the tipping point when the referendums will be held.
“Whatever the answer might be to that question, be in no doubt that change, positive change, exciting change, progressive change, is under way in Ireland.
“It is good news for Britain also because parts of the whole project of building a new island is building, renewing, consolidating that relationship that we have with our nearest neighbour.”
The recent NI Life & Times survey indicated that almost two-thirds of people in Northern Ireland believe that Brexit has increased the likelihood of Irish unity.
But, following Sinn Fein’s victory in the May Stormont Assembly elections, Taoiseach Micheal Martin said he was “amused” at speculation that it would prompt further debate about a border poll and a united Ireland, pointing out it was not the dominant issue of the campaign.