The ceasefire announcement by Oglaigh na hEireann has received a cautious welcome on both sides of the Irish border.
Sinn Fein president Gerry Adams was among the first to react.
The Louth TD said: "There can be no excuse or justification for the continued existence and operation of armed groups, either unionist or republican.
"Their continued existence leads only to hardship, loss, bereavement and imprisonment.
"There is a peaceful and democratic way forward to resolve political differences and to work towards an agreed and united Ireland."
Although the announcement means one of the deadliest dissident groups is moving away from violence, a number of other factions, including the New IRA and Continuity IRA, still continue to pose a threat.
PSNI Deputy Chief Constable Stephen Martin said: "The group has announced it is to suspend all actions against the 'British State', however, for years now, members have been heavily involved in extreme violence against people living in their own communities, including carrying out brutal beatings and shootings, as well as menacing acts of intimidation to create fear
"These vicious attacks must also be consigned to the past. It will be deeds that count ultimately, not words.
"Uppermost in my mind today are those who suffered, often most grievously, at the hands of ONH over the last decade.
"I urge ONH to live up to its commitment and also to take the further steps I've outlined.
"I would say to other groups involved in violence and criminality to follow suit and also stop immediately.
Colum Eastwood, leader of the SDLP, said the move was "long overdue".
"While we can welcome the move to cease using violence, we cannot allow for the past to be glossed over," he said.
"Let the failure of the violent campaigns of ONH and other violent actors instead serve as a hard won lesson on this island - bombs and bullets have never achieved progress.
"Again and again this island has known violence and again and again we have known its futility.
"Violence has only ever led to the hardening of hearts and the filling of graveyards.
"Today's announcement is also an opportunity for all the other fractures of dissident republican organisations to end their so-called 'campaigns'."
Meanwhile, Tanaiste Simon Coveney also welcomed the new ONH commitment.
He said: "There is no place and no justification for violence and I call on all other dissident groups to follow suit.
"We hope and anticipate that this ceasefire will be proven to be definitive and comprehensive in word and in deed."