Stormont's Deputy First Minister Martin McGuinness said should the First Minister resign it would achieve "absolutely nothing".
Asked what he thought of Peter Robinson's threat to leave his post, he said: "I have to ask the question, what would that achieve?
"It could lead to an election and Sinn Fein has no difficulty with elections ... but what would that achieve? In my view absolutely nothing."
Mr McGuinness urged politicians to "stop the grandstanding" and stressed "steady leadership, responsible leadership" is needed going forward.
The collapse of the 1982 Hyde Park bombing case has sparked a crisis in the judicial system according to Northern Ireland First Minister Peter Robinson
Mr Robinson said: "We're not on the brink of a crisis, we are in a crisis. This is a crisis. How could you have anything more than the setting aside of the proper judicial processes, where justice is not going to be done for at least 187 people?
"It is a crisis of confidence that the people of Northern Ireland will have on the policing and judicial processes in Northern Ireland and they are right to be angry."
Northern Ireland First Minister Peter Robinson has threatened to resign over the collapse of the case over the 1982 Hyde Park bombing and saying his administration have been deceived by Westminster.
Mr Robinson told UTV News he was "not prepared to remain as First Minister of an administration that kept us in the dark, that is being deceived by government, both past and present."
Northern Ireland First Minister Peter Robinson said he was "not prepared to be a stooge" for the Westminster government, accusing them of "keeping secrets" on matters devolved to the Northern Ireland Assembly.
His party, the Democratic Unionist Party, expressed his thoughts on Twitter.
Northern Ireland First Minister Peter Robinson indicated he was prepared to resign unless there was a judicial inquiry into the collapse of the John Downey case, saying:
"I have to say quite frankly that I am not prepared to be the first minister of a government that is kept in the dark on matters that are relevant to what we are doing."
Northern Ireland First Minister Peter Robinson has threatened to resign over the collapse of the case over the 1982 Hyde Park bombing.
Mr Robinson told UTV News he, "will not lead an administration where the rule of law does not prevail."
The First Minister of Northern Ireland Peter Robinson praised US Secretary of State Hillary Clinton for her "instrumental" role in the peace process.
He said: "Very often, we will sit down, and somebody will mention someone who has claimed to be instrumental in the peace process, and Martin and I look at each other, and say 'Do you know them?'
"But you are one person who has consistently helped us. You have been a great friend to Northern Ireland."
Northern Ireland's First Minister has welcomed the Prime Minister's announcement that next year's G8 summit of world leaders will be held in County Fermanagh: