The DUP has rejected Gerry Adams' claims that unionism is in crisis and instead insisted the real crisis is within Sinn Fein.
The party also spurned Sinn Fein attempts to force a rethink over Peter Robinson's withdrawal of support for the peace centre at the Maze.
As relations between the two parties continue to plummet, there are fears Sinn Fein could retaliate over the Maze U-turn by, for example, stalling progress on other key issues, including the reform of local government and the so-called shared future strategy, Together: Building A United Community.
The row deepened after Sinn Fein president Mr Adams signalled that the London and Dublin governments may have to become involved in "the problem" over the peace and reconciliation centre.
He told the Irish parliament: "The difficulties in the north are not caused by Sinn Fein.
"It is clear that there is a crisis within political loyalism and unionism."
But yesterday Mr Robinson's party alleged Sinn Fein had attempted to divert attention from a "management crisis" inside the party.
Former Stormont minister Sammy Wilson's counter-attack came after Gerry Kelly warned that power-sharing at Stormont was in crisis
"I have never been more aware of Sinn Fein MLAs talking about their discontent with decisions made by their ministers and their party leadership," the former DUP Finance Minister said.
"The only crisis in Northern Ireland politics is a Sinn Fein management crisis, where the leadership is struggling to keep all wings of the party on board.
"Gerry Kelly's bluster about a crisis in Stormont has been rightly met with almost universal scepticism, including by some in his own party.
"Whilst Adams' speech in the Dail was littered with references to leadership, it was a lot of ill-informed hot air about Peter Robinson designed to take attention away from Sinn Fein internal problems.
"Rather than Adams allowing the dissident tail to wag the Sinn Fein dog, he should tell his party members to stop trying to out-green the dissidents and concentrate on doing business in Stormont."
Relations between the two parties have been deteriorating since the Union flag dispute, as well as Mr Robinson's decision to shelve plans for the new peace centre.
Asked if there was a crisis, however, Mr Robinson said: "Of course there are big problems, and thus it has always been and we have to address those issues."
The First Minister and Deputy First Minister Martin McGuinness were said to have met for around 90 minutes on Wednesday.
STORY SO FAR
Tensions between the DUP and Sinn Fein heightened after former Sinn Fein junior minister Gerry Kelly warned power-sharing was "in crisis". Neither party is threatening to collapse the Assembly and Executive but worsening relations could spiral and endanger the prospects for the crucial Haass talks on parading, flags and the past.