The Democratic Unionist Party has claimed a border poll would be "very divisive" and polarise communities in Northern Ireland.
However, Sinn Féin says now is the time to plan and discuss the end of partition. At a seminar looking at the future of Ireland, DUP leader Jeffrey Donaldson claimed that the majority of people in the North want to remain part of the UK.
Among the other speakers at the Good Summit seminar were Sinn Féin president Mary Lou McDonald and Fine Gael TD Neale Richmond. Mr Donaldson rejected the idea of a border poll, saying the last year has shown there is a "long way" to reconciliation in the North.
"It would be very divisive," he claimed. "It would polarise the community in Northern Ireland. Right now I don't think we need to have that.
"I think that the majority of Northern Ireland wants to remain within the UK. I think that is evident from all the opinion polls that we've had.
The DUP leader added: "I think the last year has shown that we have a long way still to go in building reconciliation and bringing people together in Northern Ireland.
"I think that too should be a priority at this time."
He said there is a need to look at ways in which a shared future can be built. "I believe also that means understanding our shared history, and not being afraid to engage with our shared history."
He added that a united Ireland would not heal the wounds within Northern Ireland. As part of the Good Friday Agreement, there is a provision for holding a Northern Ireland border poll.
The Northern Ireland Act states that it would be held if the majority of those voting would want the reunification of both jurisdictions. Ms McDonald told the event that now is the time to plan and discuss the end of partition.
"Let's not rush. I'm not saying let's gallop to the polls next week and have the referendum, that clearly would be farcical," she added.
"But what I am saying is, let's not lose time now and start planning and discussing the practical bread and butter issues that matter.
"I think we need an Irish National Health Service. I think we need a universal service, free at the point of access.
"I also know that will require very considerable planning and infrastructural and a resource base, and we have to have a conversation about how we pay for that."