The Continuity IRA has rejected an invitation to talks from Sinn Fein president Gerry Adams.
Gerry Adams asked dissident republicans to meet with him
The group has also denied involvement in any plot to kill senior members of the party.
Sinn Fein's Martin McGuinness said on Thursday that the police had warned him of new threats to his life.
Dissident republican groups are opposing Sinn Fein leaders' proposals that the party backs the PSNI at a special ard fheis this Sunday.
On Thursday night, Sinn Fein leader Gerry Adams told republicans in Londonderry that if the party did support policing it would be to "put manners" on the PSNI.
He was addressing more than 1,000 people at the party's last rally ahead of this weekend's special ard fheis (conference) on policing to be held in Dublin.
The DUP's Ian Paisley Jr said his remarks were "childish and pathetic".
Mr Adams clarified that he had meant his party would "make sure they are professional, non-partisan and civic".
He said they wanted a "service for citizens who are nationalists, republicans, unionists, of different racial or ethnic backgrounds".
"We don't have it at the moment but we have the ability to get it, and that's what Sinn Fein is about," he added.
During the meeting, members of the audience expressed concern about collusion and the accountability of MI5.
There was also criticism about the decommissioning of the IRA's weapons.
Mr Adams told the crowd: "(I have asked to meet) people in armed groups which are not in cessation, one that styles itself the Continuity IRA and the other the Real IRA.
"In my opinion, there is only one IRA, and that's the one which fought the British for a very long time."
More than 2,000 republicans are expected to vote at the ard fheis this weekend.
Sinn Fein's party executive decided earlier this month to go ahead with the ard fheis.
It had earlier been put in doubt after the party complained about the lack of a "positive response" from the DUP.
The British government has said Sinn Fein support for policing and the DUP's commitment to power-sharing are essential if devolution is to be restored in Northern Ireland.
Denied CIRA links
Meanwhile, Republican Sinn Fein are considering fielding prisoner candidates in the March assembly election.
Interviewed for the BBC's Inside Politics, Republican Sinn Fein President Ruairi O'Bradaigh said he hoped young republicans would oppose Gerry Adams's support for the PSNI at Sunday's special ard fheis in Dublin.
A former IRA chief of staff, Mr O'Bradaigh outlined why he did not accept that the future devolution of justice would change the nature of the police in Northern Ireland.
"Ultimately, it is the British government which will recruit, it is the British government which will train, motivate, and above all who will pay and give the orders to such a police force," he said.
"That is already happening." Mr O'Bradaigh has consistently denied that his party is linked to the dissident paramilitary group Continuity IRA (CIRA).