The dissident republican paramilitary group, Óglaigh na hÉireann (ONH), has declared a ceasefire.
In a statement, it said that "at this time the environment is not conducive to armed conflict".
The group said it would "suspend all armed actions against the British state" with immediate effect.
The attempted murder of police officer Peadar Heffron in January 2010 was one of the most high-profile of the attacks carried out by ONH.
The group's statement does not comment on what will happen to its weapons.
In August 2010, the group said it was responsible for planting a 200lb bomb outside a police station in Londonderry, while in October a car bomb exploded outside a shopping complex in the city.
It was also behind a car bomb attack on the headquarters of MI5 at Palace Barracks in Holywood.
It is understood that a number of defectors from the Provisional IRA are involved with ONH and have helped it to develop its bomb making techniques.
PSNI Assistant 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 and control.
"These vicious attacks must also be consigned to the past.
"It will be deeds that count ultimately, not words."
Sinn Féin's northern leader, Michelle O'Neill welcomed the ONH ceasefire announcement.
"I think that all groups involved in that type of action should cease.
"Clearly, we have a pathway towards a united Ireland, a peaceful pathway and people should embrace that."
The Irish foreign minister Simon Coveney and the SDLP leader Colum Eastwood also welcomed the statement.
Analysis: Vincent Kearney, BBC News NI home affairs correspondent
This statement did not come as a surprise.
ONH announced last year that it was conducting an internal review over its future and the future of "republican struggle".
At one point, the group was the largest dissident republican organisation and was viewed as highly dangerous by the police and security services.
It carried out a number of high-profile attacks, but its activities decreased in recent years.
The organisation had been weakened by a number of factors.
It was believed to have been heavily infiltrated by informers, a number of senior members were jailed, and others defected to join other dissident groups.
The statement issued today does not mean the organisation will cease to exist.
It has declared a ceasefire, not its disbandment.
The organisation has also not said what will happen to any weapons it controls.
The fact that it has said that "at this time the environment is not conducive to armed conflict" leaves open the possibility that at some future point it could decide that the conditions are right for a return to violence.
There are currently 10 members of Oglaigh na hEireann in prisons on both sides of the border and other alleged members are awaiting trial for a range of offences.
Those who facilitated the talks that led to Tuesday's statement said they hope it will improve conditions for those prisoners - but said that progress on the issue wasn't a pre-condition for the ceasefire announcement.
Who is Óglaigh na hÉireann?
Óglaigh na hÉireann emerged around 2005, mainly based in Belfast and south Armagh, but was capable of carrying out attacks over a wide geographical area.
It carried out its first attack in 2009, a roadside bomb in south Armagh.
The name Óglaigh na hÉireann (which translates as 'Irish volunteers') has been used by a variety of groups.
It was the sole name used by a group which, for a time, became the most active dissident republican organisation.
In an interview with the Irish News in August 2010, the organisation said the "vast majority" of its members are former Provisional IRA men.
A spokesperson said they had been prepared to give Sinn Féin an opportunity to show that politics could be a substitute for violent action but had lost patience with the strategy.
He said that popular support for armed struggle was irrelevant and that Óglaigh na hÉireann would only hold talks with the British government if it was likely that they would lead to British withdrawal within a short timeframe.
Confusingly, Óglaigh na hÉireann is how all 'IRA' groups describe themselves in the Irish language, including a faction which split from the Continuity IRA in 2006 and a Real IRA splinter group, and is also the official title for the Republic of Ireland's defence forces.