However, Sinn Fein MP Chris Hazzard has said that, while his party is not calling for a referendum immediately, he argued it was “farcical” to state that it was too early to begin preparations for one.
They were responding to weekend comments by Tanaiste Leo Varadkar who said that a border poll would not be “appropriate or right” at this time.
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The DUP’s East Antrim MP Sammy Wilson agreed that a border poll would be divisive.
He told the BBC Good Morning Ulster programme: “If you observe what has happened in Scotland, of course a poll would be very divisive.
“Leo Varadkar knows it, I think the dogs in the street know that it would be divisive and I think we all know that Sinn Fein want to increase division in Northern Ireland, that is why they are now pushing for a referendum.
“I think people should note that during the election campaign they were very silent on this, they tried to present a soft face.
“Now, of course we see that Sinn Fein’s main agenda, only agenda, is the destruction of Northern Ireland.”
Mr Wilson said that Northern Ireland was “nowhere near” the conditions set out in the Good Friday Agreement for a border referendum to be called by the Secretary of State.
He added: “We know what Sinn Fein’s agenda is. It is to make Northern Ireland unstable, to call into question its very existence and planning for a referendum gives them the same impact as having a referendum itself.
“It allows them to create division, to create uncertainty about Northern Ireland’s future and to create the impression that people in Northern Ireland want this constitutional change, which of course we know they don’t.
“Any sensible person knows that Northern Ireland’s position within the United Kingdom is a far more secure economic position to have than throwing in its lot with the Irish Republic which not so long ago had to be bailed out by the United Kingdom government during the banking crisis.”
Sinn Fein recently emerged as the largest Stormont party following the Northern Ireland Assembly elections and a number of opinion polls have put the party in the lead in the Republic as well.
The party’s South Down MP Chris Hazzard said: “I don’t know of a single person who is advocating for an Irish unity referendum today, tomorrow or next week.
“What people are saying is that we need to have a conversation, we need to have planning, we need to have preparation.
“Brexit and the Tories’ chaotic approach to negotiating with Europe illustrates the importance of planning, it illustrates the importance of preparations.”
Mr Hazzard added: “We now have a situation where more people are applying for an Irish passport in the north than are applying for a British passport and I have no doubt the census figures later this year will illustrate further social and demographic change.
“That is not enough on its own to say today’s the day, let’s have a referendum, but it’s enough to say 25 years after signing the Good Friday Agreement it is beyond farcical to suggest it is too early to commence planning for a referendum.
“Let’s talk about what the future is going to look like.”
Speaking on Sunday, Mr Varadkar said the aspiration for a united Ireland was legitimate.
But he added: “I don’t think it’s appropriate or right at this time.
“Fundamentally, because I think we need to get the Assembly and Executive up and running.
“We need to resolve the issues around protocol.
“And I think that can be done.”