Sinn Fein President Gerry Adams has called on unionist leaders to ‘take a firm stand against all those who are intent on using violence and sectarianism”.
The TD made the call during an ‘away-day’ for the party’s Assembly team in Co Tyrone.
Earlier this week dissident republicans were blamed for two murders - in Belfast and Londonderry.
One man has been arrested after the murder of 39-year-old Kevin Kearney who was found shot dead in a lake in a north Belfast park.
The father-of-two had been missing since Tuesday.
Meanwhile a cross-border manhunt has been launched after the murder of 35-year-old Marry McCrory at a flat at Shipquay Street in Londonderry.
In an unusual move the PSNI said they want to interview Kieran McLaughlin, 58, in connection with the killing.
Officers requested information on the whereabouts of Mr McLaughlin - but advised members of the public not to approach him.
Mr Adams said: “The brutal slaying of two men during the week is evidence that so-called dissidents have no alternative to offer to the peace process.
“Their actions undermine the republican objective of Irish unity and they have no popular support for their activities.
“Neither can there be any justification for the continued existence of loyalist paramilitary groups that are engaged in street and sectarian violence and in criminal actions, including the sale of drugs.
“It must be made clear to those who have a tolerance for such groups, from whatever side they claim to represent, that there is a peaceful and democrat way to pursue legitimate and genuine political objectives.”
Mr Adams said there can be “no space whatsoever for criminality” and “there is no excuse whatsoever for violence”.
He added “There is also an onus on political leaders to take a firm and united stand against all of those who are intent on using violence and sectarianism.
“Regrettably the unionist leaderships have failed in this.
“They have no difficulty criticising the actions of dissidents but they are less than forthcoming when it comes to the actions of unionist paramilitaries.
“There can be no room for ambiguity on this issue. “