Mr Bruton had earlier followed his previous comparison of the republican movement to the Nazis by warning: "No more Lisburns. No more spectaculars. No more beatings. No coded warnings. Just the ballot box."
The Dail in Dublin yesterday devoted an all-day debate to the question of the peace process in the wake of Monday's double IRA bomb attack on British army headquarters at Lisburn, Co Antrim.
But amid condemnation of the IRA and Sinn Fein from all sides, Mr Bruton and other ministers conspicuously refrained from breaking all possibility of contact with the republican movement. The hope in Dublin, though it is not based on any particular confidence, is that the Lisburn attacks do not mean the peace process is at a definitive end.
But the exchanges between Mr Bruton and Mr Adams signal that Dublin's relationship with the republican movement is at its lowest ebb for years.
Mr Adams said: "Many will resent the Taoiseach's use of the terms Nazis and fascists. It would be easy for me to slip into similar name-calling but such an approach would be deeply unhelpful at this dangerous time.
"Mr Bruton has a responsibility to take the lead in creating a viable political alternative to conflict."
The Irish Foreign Minister, Dick Spring, told the Dail: "At a time like this, it is very difficult not to succumb to anger and despair. No one can avoid feeling these emotions, and the more one has worked to better the situation, the more keenly they will be felt."
Governments must make the hard decisions. "We have sought to maintain a careful balance between giving the necessary encouragement to those who are genuinely seeking a transition from violence to peace, while at the same time ensuring this cannot be exploited by those whose purposes could well be the opposite."
Police in the province are still interviewing a man arrested in the Poleglass housing estate, in west Belfast, near where the bomb gang's getaway car was found burning just after Monday's bombings. He is being questioned by the RUC at Castlereagh.