The DUP leader has cast doubt on the future of devolution and powersharing over an issue which was also raised in the strongest terms at Westminster on Wednesday.
"I'm not prepared to remain as First Minister of an administration that is kept in the dark, who were being deceived by government - and I'm talking about past and present," Mr Robinson said.
He has demanded that the current coalition government immediately rescinds all immunity assurance letters issued to so-called "on-the-runs", such as Co Donegal man John Downey.
"To this present day, no secretary of state - even though I am a privy councillor and they could have spoken to and briefed me on a Privy Council basis - nobody mentioned to me that these letters had been sent out to 187 or more individuals, as it may well turn out to be," Mr Robinson said.
We are not on the brink of a crisis - we are in a crisis. This is a crisis.
First Minister Peter Robinson
It is understood that 187 such letters were issued to terror suspects.
"This is a deliberate attempt to circumvent the courts, to allow people who are responsible for heinous crimes to come back into Northern Ireland without any fear of there being any judicial process attached to them," Mr Robinson said.
Details only emerged when an Old Bailey judge threw out the case against 62-year-old John Downey.
Mr Downey had been charged with the murders of four soldiers who died in the Hyde Park bomb in 1982, after his arrest at Gatwick Airport last year.
He was detained because his name was on the UK's most wanted list - but in 2007, despite the outstanding warrant, he had been granted an immunity deal.
He strenuously denies the charges that had been put to him.
Declaring Northern Ireland now in crisis, Mr Robinson said: "It's a crisis of confidence that the people of Northern Ireland will have on the policing and judicial processes.
"And they are right to be angry."
Mr Robinson insists that he will resign if a full inquiry into the situation is not granted - adding that, if his party had known about the immunity deals, they would not be in government today.
Meanwhile, Sinn Féin deputy First Minister Martin McGuinness has called for calm among his party's partners in government.
No sensible person will thank anyone for threatening the institutions.
Deputy First Minister Martin McGuinness
Earlier, Prime Minister David Cameron and Secretary of State Theresa Villiers were both asked separately by DUP MP Nigel Dodds in the House of Commons if they understood the seriousness of the situation.
"I completely understand the depth of anger and concern people will feel right across this country," Mr Cameron said.
"We should be absolutely clear - this man (John Downey) should never have received the letter that he received. It was a dreadful mistake.
"Whatever happens, we have to stick to the principle that we are a country and a government under the rule of law."
Nigel Dodds had questioned "how an official's letter can trump due process of law".
He has also called for the full details of all the "get-out-of-jail-free" letters to be published - including exactly how many were sent, who they were sent to, and what they said.
According to Mr Dodds, the details of the immunity deals were withheld from both Northern Ireland's First Minister and Justice Minister.
"This has very, very serious implications for devolution," he added.
I do hope, despite the long shadow this case is likely to cast, that the Northern Ireland parties will continue to work together to see if a solution can be found to the issues of the past.
NI Secretary Theresa Villiers
SDLP MP Mark Durkan also hit out at the deals that had been secured in the past, stating that "a key reason that we need to deal with the past is because we need to assure people that we haven't ended the dirty war just to end up with a dirty peace".
He added that the revelations over the Downey case "prove that some of us were right when we warned the Right Honourable Member for Neath (Peter Hain) and others that they were blighting the peace process with their penchant for side deals, pseudo-deals, sub-deals, shabby deals and secret deals - which are now doing major damage to the process more widely".
Peter Hain, former Secretary of State for Northern Ireland, stood in the chamber to insist that there had never been any question of an amnesty.
He added: "I make no apology for being part of a process that brought Northern Ireland from the hideous horror and evil of the past, into the position where old enemies have now governed for seven years in a stable, devolved government."
He added that deals had been necessary on both sides.
"Just as we had to do deals with my DUP friend sitting over there (Nigel Dodds), so we had to do deals with Sinn Féin to get to this point," Mr Hain said.
"And that was necessary for the negotiations to succeed and peace to be established."
He added: "As for the idea that this was some secret thing out of the blue - on January 11 2006, I told the House in withdrawing the legislative approach to addressing this anomaly that 'the government still believes that the anomaly would have to be faced at some stage' in the peace process."
Nobody should have been surprised that we had to do this.
Peter Hain, Labour
But Alliance MP Naomi Long questioned why the UK government had continued to send immunity letters beyond the devolution of policing and justice powers to Northern Ireland in 2010.
"This process continued after devolution," she said.
"It had profound implications for the work of the Historical Enquiries Team, for the work of the Policing Board of Northern Ireland and it continued without the knowledge of the Minister of Justice for Northern Ireland and without the knowledge of the Policing Board.
"Who administered this scheme? Who negotiated with devolved institutions behind the back of the Minister of Justice for Northern Ireland so that this scheme could continue?"
Ms Long added that letters could not be compared to the early release scheme negotiated as part of the Good Friday Agreement, as that had been voted on and accepted by the public.
Meanwhile, UUP leader Mike Nesbitt has questioned the legality of the immunity letters for suspected terrorists.
"It seems to me that, given Article 2 of the European Convention on Human Rights puts the requirement on the Government to investigate suspicious deaths, that this scheme is in breach of European Law.
"I am calling on Justice Minister David Ford to take a view as a matter of urgency."
Following the Good Friday Agreement in 1998, it was publicly accepted by the British and Irish governments that an anomaly existed in respect of those who are described as OTRs.
Gerry Adams, Sinn Féin
Sinn Féin President Gerry Adams has insisted that "both governments gave firm commitments" to deal with on-the-run cases.
"A process was put in place to deal with outstanding cases, including that of John Downey," he said.
"The arrest of John Downey by the London police was in clear breach of this and of the commitments given by the British government in 2004, during the peace process negotiations at Weston Park and in subsequent negotiations.
"John Downey should never have been arrested and this has been vindicated by the court decision."
Secretary of State Theresa Villiers has continued to insist that the collapse of the John Downey case was the result of "a grave mistake" and that an amnesty was not in place.
"It was not an amnesty and was never intended as such - there was always the recognition that, if further evidence of further offences was produced, then a prosecution was a possibility," she said.
Despite the turn of events, Attorney General Dominic Grieve is standing by his decision to charge John Downey over the Hyde park bombing and bring him before the courts.
"John Anthony Downey was arrested on 19 May 2013 at Gatwick Airport, where he was en route to Greece. On his arrest, he produced a letter stating that he was free to enter the jurisdiction without fear of arrest." he said.
"Despite that letter, he was charged by the Crown Prosecution Service with four counts of murder.
"Before he was charged my consent was sought, as the law requires, for him to face a charge of causing an explosion. I gave that consent.
"I believed then that it was right to do so and I remain of the same view today."
On Wednesday night, Theresa Villiers met with DUP First Minister Peter Robinson and Alliance Party Justice Minister David Ford separately, to discuss the situation and its implications.
What I do know is that none of these letters have issued from the Department of Justice. What we don’t know is what the implications may be for prosecutions and for our crucial efforts to find political consensus on how to deal with the past.
Justice Minister David Ford
Prior to the meeting, Mr Ford insisted that he knew nothing about the letters either and that they were not issued by his department.
"The first I became aware of this scheme and the associated letters issued was after the Downey court decision and shortly before it became public," he said.
"It was never introduced to me either before, at the point of devolution, or since devolution in April 2010.
"Comments made by the Secretary of State in the House of Commons that letters have been issued since the devolution of justice are deeply disturbing."
Urgent checks are being carried out to see if a similar case to that of John Downey could arise, as a result of one of the immunity letters having been issued.