Caoimhghín Ó Caoláin said Sinn Fein could pull out of Stormont
Sinn Féin must make it clear it wants to remain in devolved government in Northern Ireland, DUP MP Jeffrey Donaldson has said.
He was speaking after Sinn Féin TD Caoimhghín Ó Caoláin warned his party would collapse the assembly if policing and justice were not devolved.
The two parties are involved in ongoing talks over the issue.
Mr Donaldson said: "Do they want to stay in the executive? If they do, let's meet and address these issues."
Transferring policing and justice powers from Westminster to Stormont has been one of the most contentious issues since devolution was restored to Northern Ireland.
Earlier this month, it had appeared the two parties were on the brink of resolving their stand-off over the issue when they agreed there should be a single minister who should be elected by a cross-community vote.
Speaking on Sunday at a republican meeting in County Cavan, Mr Ó Caoláin said republicans were growing increasingly concerned at the lack of progress being made.
"If we are forced to conclude that change will not be forthcoming from the executive then we will have no option but to pull out our ministers and seek to put pressure where responsibility ultimately lies, which is on the British government in London," he said.
"When Sinn Fein changed our policy on policing in the north, accepting that a new beginning was being made, it was with the prospect that policing and justice powers would be transferred by May of this year.
The soundings coming from Sinn Féin at the minute are more ludicrous than ominous
"It is now the end of August and we do not even have a date for transfer. This is totally unacceptable."
Mr Donaldson said on Monday that the DUP needed to know where Sinn Féin stands on his comments.
"Bearing in mind the statement went through their official press office, one is left with the impression it's a bit of kite-flying by Sinn Féin.
"These comments were not off the cuff or out of the blue."
SDLP leader Mark Durkan said: "The soundings coming from Sinn Féin at the minute are more ludicrous than ominous.
"Are Sinn Féin saying they are going to see the assembly and North-South Ministerial Council being put back on ice?
"Are they now resorting to the kind of tactics they criticised David Trimble for, threatening to collapse the institutions as a way of trying to force movement from somebody else?"
Ulster Unionist Party leader Sir Reg Empey called on Deputy First Minister Martin McGuinness to say whether Mr Ó Caoláin was speaking for Sinn Féin ministers.
"If Martin McGuinness does not distance himself from this statement then a full-blown crisis is facing the executive next month," he said.
The Northern Ireland Assembly is currently on summer recess and is scheduled to return next month.