Sinn Fein said the DUP is pursuing policies that will create a political train wreck in Northern Ireland, as the party the party addressed republicans in Dunloy Co Antrim on Sunday.
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DUP leader Peter Robinson said he supported devolving law and order powers to the Assembly, but wants measures to boost public confidence in place first.
But as tension increased on Sunday, Sinn Fein National Chairman Declan Kearney told the republican commemoration in Co Antrim: "In recent weeks all the evidence indicates the DUP have no intention to support the transfer of policing and justice powers.
"Absolutely nothing suggests this position will change.
"Their continued intransigence is a serious political mistake. It is a train wreck political strategy and political consequences will be inevitable.
"All of this demonstrates that the impasse over policing and justice is about something deeper than a transfer of powers.
"It's about whether political unionism is prepared to co-exist with republicans in equality and partnership."
The comments came ahead of a meeting on Monday between Prime Minister Gordon Brown and Taoiseach Brian Cowen in Downing Street for talks over deadlock on the issue.
On Saturday First Minister Martin McGuinness warned a deal must be secured by Christmas if crisis is to be avoided.
Sinn Fein has said it entered government with the DUP in 2007, and changed republican policy to support the new police structures in Northern Ireland, on condition that political responsibility for policing was devolved from Westminster to the Assembly.
Republicans accuse the DUP of failing to support agreements on the timing of the move, claiming the DUP leadership is under pressure from hardliners.
Against the backdrop of political tension, dissident republicans opposed to the peace process have stepped-up their violence.
Meanwhile Mr Kearney used Sunday's republican event to repeat his party's opposition to groups that still supported the use of violence.
"A war was fought by...generations of republicans," he said. "And the IRA fought that war to a conclusion.
"There is no other IRA today. Nor is there an armed struggle to be finished. Those who choose to masquerade otherwise should disarm and disband."
The DUP has called on Government to agree to a series of moves before the party supports devolution of policing powers.
DUP leader Peter Robinson this weekend also repeated his party's preference for scrapping the power-sharing voting structures at the heart of the Stormont administration.
"In essence our proposals include the abolition of community designation and its replacement by a 65% weighted majority voting," he said.
"This would ensure widespread support was required but would not allow any single party to have a veto on progress.
"It would encourage co-operation and compromise and end the potential of blackmail by stalemate."
Sinn Fein said the proposal amounted to a return of unionist majority rule.
Mr Kearney said on Sunday: "Last week Peter Robinson asserted that the DUP will not walk away from the political institutions.
"The question is not whether the DUP will walk away. The really urgent and immediate question is whether the DUP can stay within the institutions and commit to equality and partnership.
"The DUP needs to make its mind up now."
© Press Association