The president, Mrs McAleese, said all right-thinking people would be appalled by the apparent killing of aid worker Mrs Margaret Hassan in Iraq.
He it was clear from her family's statement this evening that there must be now very grave concern for Mrs Hassan.
"I cannot begin to imagine the state of their anxiety and distress," he said.
"Those responsible for abducting Margaret stand condemned by everyone
throughout the entire international community.
"If they have any humanity, they should now bring to an end the enormous pain
and suffering that they have inflicted on an innocent and good family."
Mr Ahern said his Government's thoughts and prayers were with Mrs Hassan's
family.
Mrs Hassan's family issued a statement saying they now have to accept that their sister is "probably" dead.
The statement was issued this evening by the British Foreign and Commonwealth Office after officials in Iraq said a video apparently showing her killing was "probably genuine".
Mrs Hassan's brother and sisters - Michael, Deirdre, Geraldine and Kathryn Fitzsimons - said their hearts were broken and that there were "no excuses" for the "atrocious act".
"We have kept hoping for as long as we could, but we now have to accept that Margaret has probably gone and at last her suffering has ended," the statement said.
"Our prayers and thoughts are with our dear brother-in-law Tahseen. Margaret was a friend of the Arab world, to people of all religions. Her love of the Arab people started in the 1960s when she worked in Palestinian camps, living with the poorest of the poor and supporting the refugees.
"For the past 30 years, Margaret worked tirelessly for the Iraqi people. Margaret had only goodwill towards everyone. She had no prejudice against any creed. She dedicated her whole life to working for the poor and vulnerable, helping those who had no one else."
The statement added: "Those who are guilty of this atrocious act, and those who support them, have no excuses. Nobody can justify this. Margaret was against sanctions and the war. To commit such a crime against anyone is unforgivable.
"But we cannot believe how anybody could do this to our kind, compassionate sister. The gap she leaves will never be filled."
The Taoiseach has said those responsible for abducting the Irish-born aid worker Margaret Hassan "stand condemned by everyone throughout the entire international community".
The Fine Gael leader Mr Enda Kenny said he was "profoundly sad" to hear the reports.
"Mrs Hassan was a woman of extraordinary courage and compassion. Throughout her 30 years in Iraq, she put her faith in humanity, kindness and true goodness. Her murder would be a heinous crime and no cause is served by a barbaric murder of this nature. My concerns and thoughts are with her husband Tahseen Ali Hassan and her family," he said.
The Labour Party spokesman on foreign affairs, Mr Michael D Higgins, said it would appear Mrs Hassan has been killed by those who were holding her and he offered sympathy on his own behalf and on behalf of the party to her husband, sisters and brother. He said she was "one of the most extraordinary women I have ever met".
"The killing of Margaret Hassan is an appalling action. No cause is served by it. How could it? Margaret Hassan was somebody who gave her life to the most vulnerable people of Iraq, in the worst of times, during the sanctions, before the war, right through the most recent war and into the present period," Mr Higgins said.
"For thirty years she has been part of Iraq and for over a decade headed up one of the most important agencies providing therapeutic feeding, clean water, medicine and hospital services for those who desperately needed it. Her death will be devastating for her family and that devastation will be shared by all those who worked for her release, who hoped and prayed for it."
The aid agency Care International, for which Mrs Hassan was working when she was kidnapped almost a month ago, said is was "shocked and appalled" to learn of the apparent outcome of her abduction.
"We want to express our deepest sympathy to Mrs Hassan's husband Tahseen, and to her family. Mrs Hassan was an extraordinary woman who dedicated her life to the poor and disadvantaged in Iraq, particularly the children," the agency said.
"The whole of Care is in mourning. Through her courage, tenacity and commitment, Mrs Hassan assisted more than seventeen million Iraqis living in the most difficult of circumstances.
"Everyone who met her was touched by her personality and compassion. Care staff and volunteers will continue working around the world fighting poverty, responding to humanitarian emergencies and helping to rebuild communities.
"Care sincerely thanks the Iraqi people for everything they did to try to secure the safe return of Margaret Hassan and for the many expressions of support. Our priority now is to support Mrs Hassan's husband, Tahseen, and those most deeply affected by this tragedy."
Additional reporting: PA