The Democratic Unionist Party is seeking an emergency meeting with PSNI chief constable Sir Hugh Orde this morning concerning the murder of Paul Quinn on an isolated farm in Co Monaghan last month.
The move follows claims by the two governments' ceasefire watchdog that IRA members were involved in the murder of Mr Quinn.
The Independent Monitoring Commission (IMC) said yesterday it believed the incident in which Mr Quinn (21) was beaten and killed was a "local dispute".
However, John Grieve, one of the four IMC members and a former head of the London Metropolitan Police anti-terrorist squad, said: "despite the fact that we are saying it is a local dispute, we do believe that those who were involved in the attack on him - in his brutal murder - included people who are members or former members or have associations with members or former members of the Provisional IRA".
The Quinn family believes members of "the Provisional movement" were responsible for the murder after their son allegedly defied an order to leave the country.
Sinn Féin denied republican involvement at the time and continued to do so yesterday.
Two members of the Stormont Executive, Deputy First Minister Martin McGuinness and Regional Development Minister Conor Murphy, who is also the Newry and Armagh MP, repeatedly insisted the IRA was not responsible for the murder.
However, Lagan Valley MP and Assembly member Jeffrey Donaldson said the meeting with Sir Hugh was being sought to establish his assessment of the claims by the IMC.
"We have had information coming from south Armagh in the past couple of weeks about named individuals who, it is alleged, were involved in the murder. We are pursuing our own lines of inquiry and we want an urgent update on how the police investigation is going," he said.
He said the PSNI could help "build on the picture that is emerging". He said it was his understanding the IRA had not sanctioned the murder of Paul Quinn. "However, there may have been IRA members involved. We have to look at that, we have got to look at who these individuals are and what the nature of their involvement was."
There was unionist concern, he said, that three weeks after the murder no arrests had been made. Asked if the developments jeopardised the Executive agreement involving Sinn Féin and the DUP, Mr Donaldson said: "I'm not going to second-guess what our response will be at this stage, but if there is IRA involvement than obviously that has implications for the political process here.
"We have raised that with the prime minister, it is not something we will brush under the carpet. It will have to be dealt with. But we need to ensure that when people say they are moving on, that they are leaving violence and criminality behind, that is precisely what is happening."
In the House of Lords last night, an Ulster Unionist peer used the protection of parliamentary privilege to name a number of alleged IRA members who he said had given "permission" for Mr Quinn's murder.
Lord Laird added: "almost 20 republicans were present at the murder, as executioners, look-outs, drivers etc. Eight or nine who conducted the execution were dressed in boiler suits and wore surgical gloves. All were IRA or former IRA members."
Locals in Mr Quinn's native Cullyhanna met last night to discuss ways to deal with threats and intimidation in the area. The meeting took place in the Quinn family home. Members of four other families, whose sons have been subjected to so-called "punishment" beatings in the past, were among those who attended.
According to one of the organisers, Jim McAllister, a former Sinn Féin councillor, the purpose of the meeting was to select a committee to provide advice and support for any local person who believes they are under threat.
"This is a non-political meeting and everything to do with this committee will be entirely above board," said Mr McAllister. "If people are threatened in future in the area we will be alerting relevant local authorities - the gardaí or the PSNI".