Care International has suspended its aid operations in Iraq, after the director of the charity's work there was kidnapped.
Margaret Hassan was shown on al-Jazeera television
A video of Margaret Hassan has been broadcast on al-Jazeera TV station, showing her with her hands tied behind her back.
She was abducted by an unnamed group on her way to work in Baghdad.
Mrs Hassan's friend, film-maker Felicity Arbuthnot, described her as "an extraordinary woman".
In the UK Parliament on Wednesday, Prime Minister Tony Blair said the whole of the House was thinking of Mrs Hassan.
Several documents belonging to Mrs Hassan were shown on al-Jazeera
Ms Arbuthnot added: "Margaret is one of those slender people with a spine of steel.
"She stayed there through the 1991 war, the bombings last year, all the horrors of the embargo.
"She has tremendous presence. If there is anybody who can build a rapport with whoever these people are, she will."
Mrs Hassan's husband Tahseen Ali Hassan has told al-Jazeera the family has received no word from her captors.
Geoffrey Dennis, chief executive of Care International UK, told BBC Radio 4's Today programme: "We have heard so far nothing at all. We are doing everything we can.
"We have a lot of people on the ground locally and I am in constant contact with them trying to get updates.
Mrs Hassan, who was born in Dublin, has dual Iraqi and British nationality and has lived in Iraq for 30 years.
She was kidnapped at about 0730 (0430 GMT) on Tuesday.
Iraq has been hit by a wave of kidnappings of foreigners since 2003 for political reasons and ransoms.
But criminal gangs have also seized many local residents - notably a succession of prominent doctors and businessmen - to extort money from their families.
Robert Glasser, chief executive of Care Australia, which is co-ordinating the agency's operation in Iraq, said work had stopped since Mrs Hassan was taken.
"Our staff are not operating currently there, they're certainly not working there now in light of the current situation.
"We're unaware of any motive for the abduction and as far as we know, Margaret is unharmed at this point," he said.
"We are doing everything in our power, everything that's humanly possible to secure Margaret's release. It's a very difficult situation."
Talking to al-Jazeera, Mr Hassan said from Baghdad: "When my wife was approaching her office, two cars surrounded her vehicle.
"The kidnappers attacked the driver and took control of her car, driving off with her to an unknown destination. We haven't heard anything about the group and no one has contacted us."
He said his wife had never received any threats before the kidnapping.
"This is a humanitarian organisation which has been serving the people of Iraq for 30 years. She was well loved by everyone."
The organisation is believed to have around 30 Iraqi staff working in its Baghdad office. Foreign workers were pulled out of Iraq last November.
According to al-Jazeera, an Iraqi armed group claimed to be holding Mrs Hassan, but had issued no demands.
Pictures of Mrs Hassan's passport, credit and identity cards were also broadcast on television.
Ireland's Foreign Affairs department is working with the Foreign Office to gather information on the abduction.
In the Commons Tony Blair said everything was being done to secure her release.
Tory leader Michael Howard said his party's "thoughts and prayers" were with Mrs Hassan's family.