Arlene Foster has branded a remark by the Taoiseach that Great Britain may get fed up of Northern Ireland as "disappointing".
The First Minister was speaking on Friday after Micheal Martin said he was preparing a new Shared Island Unit for this possibility.
In an interview with the Irish Independent, Mr Martin said he plans to "beef up" the new unit so it can address a range of North/South issues and prepare for different eventualities.
"There are a two distinct political jurisdictions born out of the Good Friday Agreement - we have acknowledge the reality of that," Mr Martin said.
However, the Taoiseach said what happens in Britain impacts in Ireland and noted that English nationalism was the driving force behind the successful Brexit referendum and added that Scotland may some day break away from the UK.
"What happens if England gets turned off Northern Ireland? We've got to be thinking all this through," he added.
This prompted Mrs Foster to denounce the comments, remarking that the rest of the UK cannot "sever" its constitutional links with Northern Ireland, pointing out that a united Ireland can only be achieved with the consent of the people of Northern Ireland, as outlined in the Belfast Agreement.
"A good neighbourly north-south relationship requires consistency," the DUP leader tweeted.
"After a positive NSMC (North south Ministerial Council, the Taoiseach's comments are disappointing.
"The principle of consent determines NI's place in the UK."
The First Minister added: "Northern Ireland will keep moving forward by respecting our diverse identities not, dubious theories.
Last week Mrs Foster had said that she did not feel threatened by Mr Martin's Shared Island Unit.
"It does not threaten our constitutional position or what we believe in so I don't feel threatened at all by the shared island unit," she explained.
TUV leader Jim Allister was critical of her remarks, insisting it would be "unwise" for unionism to adopt her "laissez-faire" response to the Taoiseach's Shared Island Unit.
Speaking on Friday, Mr Allister said the plans by Dublin and nationalist parties for a united Ireland "need to be taken seriously by unionists and countered".
"The pandemic has demonstrated the benefits of Northern Ireland's place in the UK," he added.
"Unionism needs to be proactively countering the arguments of nationalism about the future, not ignoring them or dismissing them out of hand. Even the name of Mr Martin's new unit displays the narrow vision of nationalism.
"Why does Mr Martin not accept that perhaps the way to share the island of Ireland is to accept the repeatedly expressed will of the people of Northern Ireland to remain part of the UK?"