ÓGLAIGH na hÉireann's decision to call a halt to its armed campaign shows a recognition "that violence is not a bargaining chip for peace in today's society", a senior police officer has said.
Assistant Chief Constable Stephen Martin called on the group "to meet people's expectations and cease using violence immediately".
"This includes all types of organised criminality within communities," he 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 and control.
"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 ÓNH over the last decade."
Mr Martin also called on other groups involved in violence and criminality to "follow suit and also stop immediately", saying police will "continue to actively pursue and investigate those involved in acts of terrorism, violence and criminality and place them before the courts in order to protect society and keep people safe".
Tánaiste Simon Coveney welcomed the ceasefire and called on other dissident groups to make a similar commitment.
"There is no place and no justification for violence," he said.
"...We hope and anticipate that this ceasefire will be proven to be definitive and comprehensive in word and in deed."
Sinn Féin President Gerry Adams paid tribute to the "trade unionists and community leaders who were involved in securing this outcome".
"There can be no excuse or justification for the continued existence and operation of armed groups either unionist or republican," he said.
"Their continued existence leads only to hardship, loss, bereavement and imprisonment."
SDLP leader Colum Eastwood said all dissident republican groups should now "bow to the will of the Irish people".
He also said the British state had not been Óglaigh na hÉireann's only target.
"The violence of ÓNH targeted the Irish people.
"Peadar Heffron was an Irish police officer serving all the people across the north, yet ÓNH were behind his attempted murder in 2010.
"Let the failure of the violent campaigns of ÓNH and other violent actors instead serve as a hard-won lesson on this island - bombs and bullets have never achieved progress."
Bishop of Derry Donal McKeown said he "warmly welcomes" the ceasefire as "a recognition that the people of Ireland, north and south, decided 20 years ago this year to seek a way forward through exclusively political means".
"This announcement also puts the onus on our elected representatives to show that politics can deliver for the people, especially for those who are most in need. There are many decisions that need to be taken urgently," he said.
"At this time I also ask people to remember those for whom this decision has come too late. Too many people in our community will continue to bear the scars of violence for the rest of their lives.
"I commend the quiet and courageous work of all who have worked to make this announcement possible."
DUP assembly member Keith Buchanan said the ceasefire "is further demonstration of the futility of terrorism" and people should remember "the innocent victims that this organisation has made through its brutal campaign".
Alliance deputy leader Stephen Farry said the ongoing threat from dissident republicans remains, saying it had been a "qualified" statement from ÓNH which "doesn't renounce the use of violence".
