Minister for Foreign Affairs Mr Cowen and SDLP leader-elect Mr Alban Maginness have condemned the pipe bomb attack on an SDLP councillor's home in Derry overnight.
Mr Gerard Diver, his wife and four children escaped uninjured when the explosion shattered the front door and the hallway.
The RUC siad it was treating the attack as a murder attempt.
"We turned a corner in terms of political progress in Northern Ireland this week but the people who did this belong to a bygone age. Violence should be redundant," said Mr Diver.
Mr Cowen said the perpetrators would not be allowed to wreck the "new beginning" brought about by the revival of the Belfast Agreement.
"All violent acts are to be deplored but an attck on an elected representative is particularly sinister," he said.
The SDLP's Mr Maginness also condemned the bombing and offered his party's support to Mr Diver and his family.
"The concillor and his family were fortunate not to have been seriously injured or killed in this shocking attack," he said.
The attack, at Mr Diver's home at Sutton Gardens in the predominantly Protestant Waterside area of Derry happened after midnight.
The RUC, who later recovered a number of four-inch nails that had been wrapped around the device, said the family was very lucky that nobody was hurt.
Additional reporting PA