Current evidence of Provisional IRA activity is of sufficient strength to force the exclusion of Sinn Fein from Stormont's powersharing government, the DUP has insisted.
DUP deputy leader Nigel Dodds said his party would push for Sinn Fein to be thrown out of the coalition administration if the republican party did not deal with the revelations about the involvement of some IRA members in the murder of Kevin McGuigan.
Mr Dodds indicated his party would be prepared to bring down the institutions if the issue was not dealt with "very speedily".
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He led a party delegation to meet Secretary of State Theresa Villiers in Belfast to discuss the political crisis sparked by the shooting of former IRA man Kevin McGuigan and a subsequent assessment by Northern Ireland's police chief George Hamilton that the PIRA still exists and some of its members were involved in the killing.
Sinn Fein has rejected Mr Hamilton's remarks and has insisted the IRA has "gone away".
After the meeting at Stormont House, Mr Dodds said: "On the basis of what we know already there is sufficient basis on what the chief constable is saying about IRA members being involved in violence and murder and that IRA organisation exists, for an exclusion motion to be put down.
"We will continue to monitor the situation in terms of what the chief constable will say to us and what the Government and others say to us but there is no reason at all, as things stand at the moment, why there should not be the exclusion of Sinn Fein on the basis of what the chief constable has already said ."
Mr Dodds and colleagues also intend to meet David Cameron to discuss the matter.
"We raised with the Secretary of State that it cannot be 'business as usual' until this matter is resolved and she agreed with us," he said.
The DUP's main electoral rivals, the Ulster Unionists, are set to resign from the Stormont Executive next week over the furore, claiming trust in Sinn Fein has been shattered.
While the dramatic walkout by one of the three minor coalition partners will not in itself trigger the collapse of the administration, it has thrown its future into serious doubt.
It has heaped pressure on the DUP to follow suit - a move that would bring down powersharing.
Outlining the party's position after what he described as a "constructive" discussion with Ms Villiers, Mr Dodds said the DUP wanted to exert pressure on Sinn Fein to deal with the issue.
Barring action from the republican party, he said the DUP would be pressing for the support of the Government and remaining Executive parties for an exclusion motion.
If that was not forthcoming, Mr Dodds indicated the DUP would be prepared to bring down the administration itself. The Alliance Party and SDLP are not currently supporting the DUP calls for Sinn Fein's exclusion.
Mr Dodds said: "Our interest is ensuring that this matter is dealt with, that Sinn Fein are put under pressure, that they are forced to deal with this matter and that, if they don't, then they are excluded or devolved government does not continue on that basis - that is our priority, that is our objective."
He added: "We intend to keep the pressure on the government, we intend to keep the pressure on Sinn Fein, we are not going to let them off the hook, there are very serious issues they have to address - up to now they seem to be running away from those questions and we don't intend to let them run away from them. We will continue to keep the pressure on."
Announcing the UUP walkout on Wednesday, party leader Mike Nesbitt claimed his party had no option other than to withdraw from the coalition and form an opposition in the Assembly.
Sinn Fein has accused the UUP of contriving a crisis in a bid to outflank the DUP ahead of next year's Assembly poll.
The UUP has also found itself accused of hypocrisy by critics who have pointed to the fact it co-operated with political representatives of loyalist paramilitaries as part of a pan unionist/loyalist approach to a parading dispute last year.
At the weekend, police chief Mr Hamilton said that the PIRA still exists, but is not engaged in terrorism - instead pursuing peaceful, political republicanism.
But the PSNI also said some Provisional IRA members were involved in the murder earlier this month of Mr McGuigan, 53, in co-operation with a group styling itself Action Against Drugs. Detectives said there is no evidence the killing was sanctioned by the IRA leadership.
Mr McGuigan was suspected by some in the republican movement of involvement in the murder of former IRA leader Gerard "Jock" Davison in Belfast three months ago.
Police believe his killing was a revenge attack by Mr Davison's republican associates.
It is almost 20 years since the Provisional IRA's last ceasefire and a decade on from the supposed decommissioning of its weapons.
