Sinn Fein could be excluded from Northern Ireland's government after police said members of the Provisional IRA may be involved in a ruthless murder.
First Minister Peter Robinson is to hold talks with other parties about the measure before the devolved Stormont Assembly resumes next month.
He said his Democratic Unionists entered government with republicans on a commitment to exclusively peaceful and democratic means through support for the police, the courts and the rule of law as well as the dismantling of the structures of their terrorist organisation.
A DUP walkout would cause the collapse of the powersharing administration.
Police in Northern Ireland said they suspected current members of the PIRA of involvement in the murder of father-of-nine Kevin McGuigan in Belfast. Sinn Fein has vehemently rejected any suggestion the IRA had a role in the killing.
Mr Robinson said: "The basis upon which the DUP entered government with republicans was a commitment to exclusively peaceful and democratic means through support for the police, the courts and the rule of law as well as the dismantling of the structures of their terrorist organisation. That remains the basis upon which parties serve in the Executive.
"To ensure that dealing with this issue is pursued in a manner which attracts the widest possible consensus we will have discussions with other parties about tabling the necessary exclusion motion in the Assembly and asking the Secretary of State (Theresa Villiers) to intervene in circumstances where the evidence points to the IRA being involved."
Before the return of the Assembly from recess next month the DUP will seek a further update from Police Service of Northern Ireland (PSNI) Chief Constable George Hamilton to establish his conclusion regarding those responsible and the role of those in the republican movement who are associated with Sinn Fein.
Detectives have said they are not in a position to assess whether the killing of former IRA member Mr McGuigan was ordered by a command structure within the outlawed and supposedly defunct organisation.
Mr McGuigan was gunned down in east Belfast in a suspected feud between former IRA members last week.
Organisational involvement of the Provisional IRA, if proved, would have major significance for the political process in Northern Ireland. It is almost 20 years since the group called a ceasefire.
PSNI Detective Superintendent Kevin Geddes said: "A major line of enquiry for this investigation is that members of the Provisional IRA were involved in this murder."
Mr McGuigan, 53, was shot dead in front of his wife Dolores outside their home in Comber Court in the republican Short Strand last Wednesday.
He was suspected by some in the republican movement of involvement in the murder of former IRA leader Gerard "Jock" Davison in the nearby Markets area of Belfast three months ago.
There has been widespread speculation that his killing was a revenge attack by Mr Davison's one-time republican associates.
Detectives investigating the McGuigan murder have made a number of arrests and charged a man with possession of a weapon with intent to endanger life. The accused - Patrick John Fitzpatrick aged 53 from Lagmore Dale in west Belfast - was remanded in custody at Lisburn Magistrates' Court yesterday.
Mr Geddes said police were investigating whether a criminal group calling itself "Action Against Drugs" was behind the killing.
He noted that the group had issued a public statement earlier this month threatening to "execute" anyone it believed was involved in the Davison murder.
"We have a main line of enquiry that Kevin McGuigan was murdered by members of Action Against Drugs in what they believe to have been in revenge for the murder of Jock Davison," he said.
Mr Geddes said while Action Against Drugs was made up of "criminals, violent dissident republicans and former members of PIRA" he said current members of the PIRA are also suspected of involvement in the murder. But he insisted Action Against Drugs was a "separate" organisation from the PIRA.
The officer added: "It is my assessment at this stage and my belief that people who are members of the Provisional IRA were involved in this murder, but we will not speculate on at what level."
He added: "I have no information at this stage to say whether this was sanctioned at command level or not and I am not prepared to speculate on that."
The IRA has been on ceasefire since 1997 and decommissioned its weapons in 2005.
Sinn Fein Deputy First Minister Martin McGuinness tweeted: "The people who murdered Jock Davison are criminals. Those who murdered Kevin McGuigan are also criminals. They must be brought to justice."
Senior Sinn Fein member Gerry Kelly said: "Sinn Fein has called consistently on people to support the PSNI investigations into the killings of Kevin McGuigan and Gerard Davison.
"The killing of Gerard 'Jock' Davison was wrong and nothing to do with republicanism. Equally the killing of Kevin McGuigan was wrong and nothing to do with republicanism.
"These killings need to stop now.
"The PSNI have said that the Action Against Drugs group threatened to kill anyone involved in the killing of Gerard Davison only days before the killing of Kevin McGuigan.
"I am on record as saying, and I repeat, this is a criminal gang which has been involved in extortion, intimidation and murder in nationalist communities."