Unionists have warned Sinn Féin president Gerry Adams that his call for a referendum on a united Ireland is divisive and destabilising.
The republican leader told a party meeting in the Republic that a vote on partition is winnable in the next five years.
But with power-sharing in the north deadlocked for months and talks on reviving Stormont in the balance, DUP leader Arlene Foster said the prospect of a border poll is not sensible.
"Northern Ireland needs stability," she said.
"That means we need a functioning government to make vital decisions. We do not need a divisive and destabilising border poll."
Ms Foster dismissed the idea and said the argument over the north's place in the UK is not about money but about the influence its language, music, literature, arts and sporting success projects around the world.
"There will be no border poll as there is no evidence of overwhelming support for a united-Ireland. Holding, or indeed even just proposing, a border-poll within five years is not sensible," she said.
"It will propel Northern Ireland into a cycle of referenda. This is nothing short of wishful thinking by Gerry Adams."
Ms Foster described Mr Adams' call as a "narrow political project".
And she added: "It is time he and those around him lifted their eyes and considered the damage recent instability is having upon everyone in Northern Ireland."
The debate about a border poll was thrown into the mix as Ireland's Foreign Affairs Minister Simon Coveney held meetings with political parties in Belfast on the prospects for reviving power-sharing.
Mr Adams said the referendum on partition should be government policy in the Republic.
He said: "In the North, both the DUP and the British government continue to refuse to agree that the Executive and the Assembly be restored on the basis of equality, respect and integrity for all.
"They also disrespect and ignore the vote of people in the north in the Brexit referendum and are insisting on dragging the North out of the EU against the wishes of the electorate."
"In fact, the DUP have torn up propositions being developed with Sinn Féin and others on Brexit in favour of the Tory government's little Englander approach."
Secretary of State James Brokenshire said on Monday that financial pressure on the north's health service could force the British government to step in if power-sharing is not resurrected soon.
All party leaders agree on the need for devolution.
But Sinn Féin are holding fast to demands for an Irish language act to enshrine the rights of Irish speakers in the north.
Power-sharing has been in deep freeze since early this year when the late Sinn Féin deputy first minister Martin McGuinness resigned in protest at the DUP's handling of a botched green energy scheme which risks landing the taxpayer with millions of pounds of debt.
It has been seven months since Stormont ministers took decisions, and political negotiations were paused over the summer.
Health trusts recently unveiled £70 million of cost-saving proposals.
