First Minister Peter Robinson has said that if police find the IRA responsible for Kevin McGuigan's murder, Sinn Fein must leave Stormont.
Sinn Fein spokesman said: "All our public representatives are urging people to fully co-operate with the police in this investigation, including giving them information."
It is understood that former IRA activist Mr McGuigan (53) had been blamed by an IRA inquiry for murdering his former friend Gerard 'Jock' Davison in May.
Mr Robinson said: "There is an indication that some of Davison's former friends were involved in this murder as a crime of retribution. We will obviously be wanting to talk to the police once they have had an opportunity to investigate because, if there was any organisational involvement, that would have repercussions for the political process."
He bluntly spelt out the consequences of the IRA being "organisationally involved".
"It would be the end of Sinn Fein's involvement at the Assembly. Under the legislation, the Assembly or the Secretary of State would have to take action," he said.
"I note Sinn Fein's condemnation of the act, but let's see the independent investigation of the police and who they find responsible.
"Fear about the impact on the political process should not be a determining factor in whether the police point the finger.
"The processes of justice should be allowed to take place regardless.
"Sadly, there are some people who think they can dispense justice themselves in the way that they see fit, and that is just unacceptable in our society."
Sinn Fein itself has been loud in its condemnation of the shooting.
Paul Maskey, the MP for West Belfast, dismissed talk of the IRA being responsible.
"I don't believe or accept for one second that the IRA has been involved in this at all, it just doesn't register," he said.
"What I am concerned about is unhelpful speculation."
Gavin Robinson, the DUP MP for East Belfast, said there was no justification for the killing.
He said: "Mr McGuigan clearly had a past, but if there was any connection between recent events, it should have been dealt with by the police - and no one else."
Deputy First Minister Martin McGuinness unreservedly condemned the "appalling deed", while SDLP leader Dr Alasdair McDonnell - who had been the McGuigan family doctor - said: "My thoughts are with the family of the man shot dead."