The people who are sheltering violent groups should end their support for the futile loss of life, Gerry Adams has said.
The Sinn Fein president said republican heartlands were "seething with anger" at what he branded "a small core of anti-peace groups" responsible for attacks including the murder of Catholic policeman Ronan Kerr.
The republican leader repeated his offer to meet the breakaway factions in a bid to persuade them to support the peace process.
"The people of this island demand that you stop," Mr Adams wrote in his blog, Leargas.
"I am prepared to meet you anywhere at any time to listen to what you have to say and to tell you that there is now a democratic peaceful way to unite our people and our country on the basis of equality.
"Your achievement has been to unite us all in opposition to your actions. It is time to end these futile attacks on the peace process, they will not succeed."
In a further challenge to sections of republicanism, he added: "I would also like to address the small number people who might have some tolerance for armed actions. To those who might shelter or provide resources and facilities to the perpetrators of these actions you need to ask yourselves what purpose is being served?
"Don't be fooled into thinking that you are helping the IRA. The war is over. The IRA is gone. The IRA embraced, facilitated and supported the peace process. When a democratic and peaceful alternative to armed struggle was created the IRA left the stage."
Mr Adams said international experience showed that, despite the emergence of a peace process, some remain wedded to violence for their own ends.
"This is not a new phenomenon nor is it uniquely Irish. However some of these people who are masquerading as activists and others who support violent anti-peace actions are heavily involved in extortion, robberies, and tiger kidnappings in republican heartlands," he said. "Sinn Fein is totally committed to exposing this activity and to making a stand against them."