IRA ceasefire: McGuinness urges dissidents to end conflict
Sinn Féin's Martin McGuinness has urged dissident republicans, on the IRA ceasefire 20th anniversary, to "take that same step into politics and away from conflict".
Mr McGuinness said there could be "no return to the violence and repression that scarred this society for so long".
Gary Donnelly, a member of the 32 County Sovereignty Movement, said he did not believe the appeal would work.
The republican group is opposed to the peace process.
Mr McGuinness made his comments at an event in Londonderry on Sunday.
"In 1994, dialogue offered the only way out of perpetual conflict and Irish republicans entered that dialogue confidently," he said.
He said there was no need for violence.
"Successive agreements supported by the vast majority of the Irish people have removed any rationale for armed struggle and have put in place peaceful and democratic alternatives," he said in a keynote speech in Londonderry on Sunday.
The former IRA commander has been Northern Ireland's deputy first minister since 2007, following a power-sharing agreement between Sinn Féin and the Democratic Unionist Party (DUP).
In his speech to about 300 republicans in the Creggan area of the city, Mr McGuinness criticised the DUP.
"The absence of dialogue and a commitment to dialogue as the way to overcome disagreements is at the heart of the growing difficulties we are now facing in the peace process across a range of key issues," he said.
He said the "real threat to the political institutions is stagnation and the absence of progress".
"I have personally tried to understand and reach out to the unionist population not least in my engagements with Queen Elizabeth," he said.
"But reconciliation is not a one-way street - unionist leaders need to engage in similar initiatives.
"So there is an enormous onus on those who recognise the enormous progress we have made, and continue to make, since the IRA cessation in 1994 to make their voices heard."
Mr Donnelly, who was elected as an Independent to the new 'super council' in Derry and Strabane, said he could not speak on behalf of armed groups, but said he did not think Mr McGuinness would be listened to.
"I would doubt it very much. I would be very, very sceptical," he said.
"To sort out the age old conflict in Ireland, then the issues which brought about that conflict, which is the violation of Irish sovereignty, has to be dealt with.
"And unless these armed groups are interested in selling their soul and getting a chance to meet and greet presidents, Queens and Israeli ambassadors, then by all means, but if there is to be dialogue then it needs to be dialogue dealing with the issues that caused the conflict in Ireland."