A Sinn Féin MLA says the people who killed Kevin McGuigan are 'criminals', not Republicans. He says he does not believe the IRA was involved.
The comments from Alex Maskey come after police in the North arrested another person in connection with the murder of the 53-year-old in Belfast last week.
The PSNI says it believes Provisional IRA members were involved in killing Mr McGuigan, as part of the Action Against Drugs group.
Meanwhile, the North's First Minister Peter Robinson is to hold talks with other parties about the possible exclusion of Sinn Fein from Northern Ireland's government before the Assembly resumes next month.
He said his Democratic Unionist Party entered government with republicans on a commitment to peaceful and democratic means through supporting the police and the courts and also dismantling structures of their terrorist organisation.
A DUP walkout would cause the collapse of the administration at Stormont. Sinn Fein has rejected any suggestion the IRA had a role in the killing of Mr McGuigan.
There has been speculation the 53-year-old man was killed in a revenge attack amid a suspected feud between ex-IRA members.
If it is proved there was organisational involvement of the Provisional IRA (PIRA) in the McGuigan killing, it would have major significance for the political process in Northern Ireland.
The group called a ceasefire nearly 20 years ago and it decommissioned its weapons in 2005.
Police Service of Northern Ireland (PSNI) Detective Superintendent Kevin Geddes said: "A major line of enquiry for this investigation is that members of the Provisional IRA were involved" in the McGuigan murder.
But detectives said they were not in a position to assess whether the killing was ordered by a command structure within the outlawed and supposedly defunct organisation.
Mr McGuigan was suspected by some in the republican movement of being involved in the murder of former IRA leader Gerard "Jock" Davison in the nearby Markets area of Belfast in May.
And this led to speculation Mr McGuigan was killed by Mr Davison's one-time republican associates.
Mr Geddes said police were investigating whether a criminal group calling itself "Action Against Drugs" was behind the McGuigan 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.
'They have to be brought to justice'
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.
Last week, Peter Robinson warned Sinn Fein it will face expulsion from the Stormont Executive if IRA involvement in the McGuigan murder was proved.
However, Sinn Fein has rejected the suggestion the IRA had a role in the killing.
After the PSNI announcement, 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".
Detectives investigating the McGuigan murder have made a number of arrests and have charged a 53-year-old man with possession of a weapon with intent to endanger life.
The accused - Patrick John Fitzpatrick from Lagmore Dale in west Belfast - has been remanded in custody at Lisburn Magistrates' Court.
Alex Maskey is the Sinn Fein MLA for west Belfast.
He told Newstalk Lunchtime Sinn Féin 'rejects' the activity of Action Against Drugs - and says the IRA was not involved.
While Jeffrey Donaldson, MP with the Democratic Unionist Party, told Newstalk Breakfast that he is convinced members of Sinn Fein know what happened.
