Prime Minister David Cameron has also ordered a judge-led review into controversial government letters issued following the 1998 Good Friday Agreement which allowed terrorists to escape prosecution.
Critics have branded the "On The Runs" letters "get out of jail free cards" for Republican paramilitaries and they led Northern Ireland First Minister Peter Robinson to threaten his resignation unless those involved and their crimes were identified.
Yesterday he backed down after being reassured by the UK Government that the documents are now worthless and winning the other part of his ultimatum, for a judicial inquiry. He said the alleged terrorists would sleep "less easy tonight".
Mr Robinson told a press conference: "I welcome the judge-led inquiry that he announced and I am happy with the terms of reference that have since been set out."
He added: "I think the Prime Minister and the secretary of state have been prompt, they have dealt with the issues seriously and in a manner that is satisfactory to me.
"So yes, I do not intend to resign on the basis that if you get what you want why on earth would you want to resign?"
The row engulfed the Stormont Government after Wednesday's collapse of the case against John Downey, 62, of Donegal, for the Hyde Park bombings in 1982.
He had been charged with the attack which killed four members of the Royal Household Cavalry. He denied any involvement.
The details of the documents emerged in court and Mr Robinson threatened his resignation on Wednesday unless all of the 180 or so suspects and the crimes they are linked to were identified and there was a judicial inquiry.
Sinn Fein's Martin McGuinness, Northern Ireland's Deputy First Minister, said the Government could not overturn what had been a lawful process of assuring suspects they would not face prosecution.
Mr Robinson's Democratic Unionist Party (DUP), claim they were kept in the dark about the scheme, the result of a deal between Sinn Fein and the last Labour government.
With the deadline for Mr Robinson's resignation looming, and keen not to destabilise the peace process in Northern Ireland, ministers acted. They said they will now make clear to all involved that if evidence exists, or emerges, which links them to an offence they could be questioned and potentially prosecuted.
Mr Robinson welcomed the move. He said: "That makes it clear that (the suspects now) have a fairly worthless piece of paper."
Earlier Mr Cameron had been pressed on whether or not he thought the "comfort letters" to those on the run had been a mistake.
He said: "Difficult decisions were taken around the time of the Good Friday Agreement and around the time of the peace process. As an incoming Prime Minister I don't want to unpick or call into question all those difficult decisions that were made.
"I want to be a Prime Minister who helps deliver devolved institutions in Northern Ireland, continued peace and progress in Northern Ireland.
"But I want to be clear to people that these letters were not and should not be any form of amnesty, and that's why this (inquiry's) report is so important."
He added that he accepted calls for a "full, independent examination" of the process.
The letters were part of a deal between Sinn Fein and the last Labour administration.