The Taoiseach, Mr Ahern, has described today's events in Russia as a "nightmare".
Mr Ahern said Irish "hearts go out to all the families and the children" and expressed his hope that casualties could be kept to a minimum.
The Minister for Foreign Affairs, Mr Cowen, said today it was deeply regrettable that a peaceful resolution could have been found to the Russian hostage drama. The hostage-takers "clearly had no regard for human life", he said.
"Their actions have served no purpose, other than to bring violence, fear and grief into the everyday lives of ordinary people. These actions must be condemned by all right-thinking people.
"I want to offer my most sincere condolences to the families and friends of those killed, and to the Russian people."
The Labour Party and Fine Gael also condemned the kidnappers' actions.
Mr Ruairi Quinn, Labour's Euopean Affairs spokesman, described the scene as "tragedy of unimagined proportions".
"The scenes of children fleeing the school bloodied or being carried away on stretchers adds to the horror," he said. "My only hope is that the final death toll proves to be much smaller than currently anticipated."
Fine Gael's foreign affairs spokesman Mr Gay Mitchell said the kidnapping was a "barbarous act which has done nothing for the cause of Chechen separatists". He said the International Criminal Court should be specifically empowered to try the perpetrators and organisers of such atrocities.
UNICEF said the siege "represents a new and discouraging low - children used as hostages and denied food and water for three terrifying days."
Ms Maura Quinn, Executive Director of UNICEF Ireland, said: "Children must never be used for political purposes and schools must never be degraded to places of violence.
"If we don't respect the sanctity of childhood, then we have nothing."