However, Justice Minister Alan Shatter said Mr Adams’s offer to mediate should be seen in the light of the upcoming elections in Northern Ireland.
The Sinn Féin Dáil leader called on the legitimate political organisations representing dissidents to say “stop” to violence.
“These people missed the revolution. The objective must be to get those groups to stop their activities if they want to get involved in republican politics and there are peaceful and democratic ways in which they can be involved,” he said.
The intervention came after a 500lb van bomb was discovered by police near Newry in the wake of the murder of Catholic PSNI officer Ronan Kerr in Omagh. His killing inspired a mass protest for peace at the weekend.
Dissident republicans opposed to the peace process were blamed for the murder and the van bomb attempt.
Mr Adams called on dissident republican groups like the 32 County Sovereignty Movement, Éirigi, Republican Sinn Féin and the Republican Network for Unity, to condemn the killing of Mr Kerr.
Éirígí general secretary Breandán MacCionnaith claimed Mr Adams was trying to demonise his party.
“Éirígí’s position on the recent killing in Omagh and on other armed actions is clear and unambiguous. The party is not aligned to or supportive of any armed groups or their actions. This has been our position since our foundation five years ago,” he said.
Three people remain in custody in connection with the police investigation into the attack.
A 33-year-old man was arrested in Omagh on Friday and police were also given five more days to question a 26-year-old man arrested in Scotland on Wednesday and re-arrested on Thursday, plus a 40-year-old man who was arrested near Omagh on Thursday.
Mr Adams said it was wrong to brand the people responsible for the upsurge in violence “republican dissidents” as they had an anti-peace agenda.
Mr Adams, who branded Queen Elizabeth’s upcoming visit “premature” said republicans should mark the occasion peacefully.
Meanwhile, Mr Shatter said Mr Adams first made the offer to mediate in a debate in the Dáil on the murder of Mr Kerr.
“I am not convinced talking to these people [dissident republicans] would make any difference. They are engaged on a futile campaign of violence.
“Of course it is up to Gerry Adams to make judgments as to what he should do. If he has made the offer again this week and last week I do not know if anything could come of this meeting and I am not optimistic that these people are interested in engaging with anybody,” he said.
“I presume he’s genuine in the offer he is making but we should never forget that the offer is made in the context of the backdrop of the Northern Ireland elections.”
He said the only option was in supporting the Garda and the PSNI in “relentless targeting of this group who have been involved in atrocities and to bring an end to the murderous campaign that these terrorists are intent on engaging in”.