The Minister for Foreign Affairs has described the makers of the bomb found in Co Cavan as"enemies of the people".
An Army explosives team is continuing its operation to clear the area near the Border where a milk churn full of explosives was found on Sunday night.
Mr Cowen said the dissident republicans thought to be responsible were a small criminal minority who would be dealt with through the legal process.
He said: "These people who are insistent on carrying on attempts at attacks on life and property represent nobody and they are simply enemies of the people.
"There are still some - albeit a small minority - who try to give the impression that they are acting on others' behalf.
"They are simply a criminal element who have to be dealt with according to our laws."
Gardaí are also conducting a follow-up search of the area around a field in the townland of Clonoula, a mile off the Cavan to Clones road, where the bomb - thought to hold up to 1,100 lb of explosive - was found. The locationis about 500 yards inside the Republic.
It is believed the bombwas being prepared by dissident republicans for an attack on Northern Ireland security forces ahead of political talks due to take place this week over the stalled peace process.
Gardaí believe the would-be bombers telephoned a hoax bomb warning in Clones on Sunday night in an effort to hamper the search for the bomb at Clonoula.
Mr Cowen added: "I want to congratulate our security forces for ensuring that this product was not brought to its ultimate destination, wherever that might have been.
"It is indicative of the very strong hand that has been taken by our security forces in these matters and I hope that they can continue to have continued success.
"It is a reminder to us all that the only way of solving all these problems is peacefully and through the political process."
Additional reporting PA