Mrs Hassan had lived in Iraq for 30 years and married an Iraqi
Political leaders have condemned the apparent murder of aid worker Margaret Hassan by her kidnappers in Iraq.
Tony Blair said it was "abhorrent", while Irish premier Bertie Ahern said her kidnappers "stand condemned by... the entire international community".
Mrs Hassan's husband has begged for the return of the body of his wife, who had Irish, British and Iraqi nationality.
A video showing a blindfolded woman being shot in the head has surfaced and has been checked by experts.
UK Foreign Secretary Jack Straw said they had concluded Mrs Hassan had "probably" been murdered.
He added: "To kidnap and kill anyone is inexcusable.
We now have to accept that Margaret has probably gone and at last her suffering has ended
"But it is repugnant to commit such a crime against a woman who has spent most of her life working for the good of the people of Iraq."
Mrs Hassan, 59, had lived in Iraq for 30 years.
She was seized by an unknown group in the Iraqi capital on 19 October.
Arabic TV news channel Al Jazeera said on Tuesday it had had a copy of the videotape showing her apparent killing for several days, but had chosen not to broadcast it.
The video apparently shows a man firing a pistol into the head of a blindfolded woman wearing an orange jumpsuit.
A spokesman for Al Jazeera said he presumed the woman was the kidnapped aid worker.
Mrs Hassan's husband Tahseen has appealed to the kidnappers to return his wife's body.
He said: "I beg those people who took Margaret to tell me what they have done with her.
Mr Hassan made an emotional plea for her body to be returned
"They can tell me. They can call the helpline. I need her. I need her back to rest in peace."
Mrs Hassan's sisters and brother, Deirdre and Kathryn - who live in London - and Geraldine and Michael Fitzsimons, said in a statement their "hearts are broken".
They said: "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.
"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."
After Mrs Hassan was kidnapped, the aid worker's colleagues and family repeatedly pleaded for her release.
Canon Andrew White, who founded the Iraqi Centre for Dialogue, Reconciliation and Peace in Baghdad, was also involved in negotiations to get Margaret Hassan freed.
He told BBC Radio 4's Today her probable murder showed terrorism and the insurgency in Iraq was "totally out of control".
Margaret Hassan's life and the memory of her work will remain in millions of people's hearts for generations to come
"I doubt whether there's anybody else who has been so committed to Iraq and the people of Iraq for so long - she was almost revered in Iraqi society," he said.
Canon White pointed out that even the group led by extreme militant Abu Musab al-Zarqawi had apparently called for Mrs Hassan's release.
But he added: "We've got so many renegade new kind of terrorist operations that some of them have absolutely standards at all - that they would be willing to kill somebody who, in essence, was an Iraqi who has helped Iraqis for many years."
Mrs Hassan was filmed by her captors asking Tony Blair to pull British troops out of Iraq.
Mrs Hassan was driving to her job as director of Care International's Iraq operations when she was seized. The agency has since halted work in the country.
If her death is confirmed, she will be the first foreign female hostage to have been murdered in Iraq amid a recent wave of hostage-takings
I hope we will now have a minutes silence in this country like we did for ken bigley surely this lady was equally as worthy?
No? I doubt it too
Political leaders have condemned the apparent murder of aid worker Margaret Hassan by her kidnappers in Iraq.
Tony Blair said it was "abhorrent", while Irish premier Bertie Ahern said her kidnappers "stand condemned by... the entire international community".
Mrs Hassan's husband has begged for the return of the body of his wife, who had Irish, British and Iraqi nationality.
A video showing a blindfolded woman being shot in the head has surfaced and has been checked by experts.
UK Foreign Secretary Jack Straw said they had concluded Mrs Hassan had "probably" been murdered.
He added: "To kidnap and kill anyone is inexcusable.
We now have to accept that Margaret has probably gone and at last her suffering has ended
"But it is repugnant to commit such a crime against a woman who has spent most of her life working for the good of the people of Iraq."
Mrs Hassan, 59, had lived in Iraq for 30 years.
She was seized by an unknown group in the Iraqi capital on 19 October.
Arabic TV news channel Al Jazeera said on Tuesday it had had a copy of the videotape showing her apparent killing for several days, but had chosen not to broadcast it.
The video apparently shows a man firing a pistol into the head of a blindfolded woman wearing an orange jumpsuit.
A spokesman for Al Jazeera said he presumed the woman was the kidnapped aid worker.
Mrs Hassan's husband Tahseen has appealed to the kidnappers to return his wife's body.
He said: "I beg those people who took Margaret to tell me what they have done with her.
Mr Hassan made an emotional plea for her body to be returned
"They can tell me. They can call the helpline. I need her. I need her back to rest in peace."
Mrs Hassan's sisters and brother, Deirdre and Kathryn - who live in London - and Geraldine and Michael Fitzsimons, said in a statement their "hearts are broken".
They said: "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.
"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."
After Mrs Hassan was kidnapped, the aid worker's colleagues and family repeatedly pleaded for her release.
Canon Andrew White, who founded the Iraqi Centre for Dialogue, Reconciliation and Peace in Baghdad, was also involved in negotiations to get Margaret Hassan freed.
He told BBC Radio 4's Today her probable murder showed terrorism and the insurgency in Iraq was "totally out of control".
Margaret Hassan's life and the memory of her work will remain in millions of people's hearts for generations to come
"I doubt whether there's anybody else who has been so committed to Iraq and the people of Iraq for so long - she was almost revered in Iraqi society," he said.
Canon White pointed out that even the group led by extreme militant Abu Musab al-Zarqawi had apparently called for Mrs Hassan's release.
But he added: "We've got so many renegade new kind of terrorist operations that some of them have absolutely standards at all - that they would be willing to kill somebody who, in essence, was an Iraqi who has helped Iraqis for many years."
Mrs Hassan was filmed by her captors asking Tony Blair to pull British troops out of Iraq.
Mrs Hassan was driving to her job as director of Care International's Iraq operations when she was seized. The agency has since halted work in the country.
If her death is confirmed, she will be the first foreign female hostage to have been murdered in Iraq amid a recent wave of hostage-takings
I hope we will now have a minutes silence in this country like we did for ken bigley surely this lady was equally as worthy?
No? I doubt it too