First Minister Peter Robinson has said those responsible for sending a letter bomb to Secretary of State Theresa Villiers "will not further any aim or objective by their vile and callous deeds".
The Stormont Castle headquarters of Peter Robinson and Martin McGuinness near Belfast were evacuated on Tuesday afternoon after a viable letter bomb - addressed to Ms Villiers - was intercepted.
During the alert, Mr Robinson was moved to Parliament Buildings in Stormont - his work and meetings continued unaffected.
Police later confirmed the device - discovered at around 10.30am - was a viable letter bomb similar to those found elsewhere in recent days.
Condemning the threat, Peter Robinson said "those responsible for sending this, and other devices, through the post have absolutely no regard for the lives of postal workers and staff working in offices".
"They will not further any aim or objective by their vile and callous deeds," he said.
"Northern Ireland will not be dragged back by terrorists who have nothing but misery to offer."
Because the Assembly is in recess, Mr McGuinness was not in Stormont Castle.
Dozens of staff were evacuated during the alert, many of them also moving to Parliament Buildings.
Two letter bombs were recently sent to the police, one in Londonderry and the other to the chief constable of the Police Service of Northern Ireland. Another was posted to the Public Prosecution Service in Londonderry.
Dissident republicans were blamed.
Ms Villiers is in London today, meeting former US diplomat Richard Haass about progress on talks he is chairing with Northern Ireland politicians about boosting the peace process.
Theresa Villiers condemned those responsible for the letter bomb.
"I utterly condemn the attempted attacks we've seen over recent days," she said.
"If those responsible think that this kind of criminal activity will further any agenda, then they are completely mistaken."
Mr Robinson and Mr McGuinness recently returned from a trade mission in the US.
Yesterday, a letter bomb was delivered to the offices of the Prosecution Service in Londonderry - the third device to be sent through the post.
A stretch of the city's Limavady Road was sealed off for a time after Army explosives experts were called to the offices at Foyle Chambers, which had to be evacuated by staff.
Last Friday, similar devices were discovered addressed to Police Service of Northern Ireland (PSNI) Chief Constable Matt Baggott and Chief Inspector John Burrows, the police commander in Derry.
Republicans opposed to political power-sharing have been blamed.
Dissident republicans are also believed to have been behind two other bomb attacks on police last week. Officers escaped injury when pipe bombs were thrown at patrol vehicles in Newtownabbey, Co Antrim, and in Derry city centre.
Dissidents also claimed responsibility for firebombing a shop in Belfast city centre recently.
The threat from extremists opposed to the peace process has been deemed severe by the Home Office. They have been responsible for the deaths of two soldiers, two police officers and a prison guard in recent years.
There are few MLAs at Parliament Buildings because of the Assembly recess.
Stormont's Justice Minister, David Ford, thanked staff in Royal Mail sorting offices for their vigilance when handling suspicious packages.
He visited the sorting office at Mallusk, near Belfast , where staff recently intercepted a viable explosive device addressed to the Chief Constable. On the same day, staff at the Lisburn sorting office intercepted another device addressed to the senior police officer in Londonderry.
Mr Ford said: "There are delivery offices across Northern Ireland handling many thousands of letters and parcels every day. Royal Mail has been very active in putting in place security measures to detect and deal with suspicious packages, which in turn helps to secure and protect our citizens.
"I was grateful for the opportunity to personally thank some of the staff involved in dealing with our mail and carrying out those security checks. There is an obvious threat to these staff when reckless people abuse the mail system and I commend them for their vigilance."
Mr Ford condemned the attempted attack on Ms Villiers.
"This is yet a further attempt to attack a public figure," he said. "Do those sending these devices really think their intended target will personally open the package? Their actions are to be condemned by all right-thinking people."