Border poll: NI Parties are divided over Enda Kenny's comments
Sinn Féin leader Gerry Adams has said there is "a need to be open and imaginative" on new constitutional arrangements.
He welcomed Taoiseach (Irish prime minister) Enda Kenny's comments on a possible referendum on Irish unity.
DUP MP Ian Paisley said Mr Kenny was "being mischievous".
The taoiseach said Brexit talks should consider that a clause in the Good Friday Agreement could result in the calling of a referendum.
In his remarks to reporters on Monday at the annual MacGill Summer School in Glenties, County Donegal, Mr Kenny said the triggering of a border poll required "clear evidence of a majority of people wishing to leave the UK and join the Republic".
He added: "It may be, in the eyes of some, a fanciful theory but who knows what happens in 10, 20 years time?"
Adams responded by calling for all parties supporting a united Ireland "to discuss how best this can be achieved."
"In the context of the north being dragged out of the EU by England, there is now a greater opportunity to achieve this," he said.
North Antrim MP Mr Paisley said Secretary of State James Brokenshire and his predecessor, Theresa Villiers, had both ruled out holding a referendum.
"It's not going to happen," he said.
"We all know in the next nine months Enda Kenny is not going to be taoiseach. So, he's really just being mischievous.," Mr Paisley added.
Ulster Unionist MLA Jenny Palmer described Mr Kenny's comments as "much ado about nothing".
She said that, in the wake of the EU referendum, the Stormont executive's priority should be "to convince the people of Northern Ireland that they have a plan for the way forward for our economy, our farmers, our voluntary and community groups, our universities and everyone else who depends heavily on EU funding and support."