Aljazeera received a video from the group saying it would hand over Margaret Hassan to al-Zarqawi's group within 48 hours. It broadcast a video with a masked man speaking but there was no audio.
Aljazeera spokesman Jihad Ballout said: "Yes, we have received a tape, but we decided not to air it because we believe it's too graphic."
Irish Prime Minister Bertie Ahern told lawmakers the tape, which was described to him, shows the 59-year-old Care International aid chief pleading for her life directly to camera before fainting.
He described the video's contents as "distressing".
A spokesman for Ahern later said the premier had received second-hand reports of the video and had not seen it himself. He said the contents, as described, showed Hassan fainting, having a bucket of water poured over her to revive her, then lying wet and helpless on the ground before getting up and crying.
"There were a number of very dangerous and very serious time scales stated," Ahern said, without elaborating.
A government spokesman said he could not confirm whether Ahern was referring to a possible threatened execution date for Hassan or any other threats made by her captors.
The British news agency Press Association reported that Hassan's family had seen the film and immediately arranged to meet Ahern.
Earlier on Tuesday, Ahern met Hassan's three sisters and issued a joint appeal for her release.
A description of the video was
given to Ahern
Standing beside the prime minister, Hassan's sister Deirdre Fitzsimons addressed her sibling's captors directly.
"We are the Irish family of Margaret, and we are pleading with you to set her free," she said.
"We have listened to your demands and begged [Prime Minister] Tony Blair and the British government to release the women prisoners and also not to move the troops," she said, referring to Britain's redeployment of several hundred troops north towards Baghdad this week at US request.
"But we are Irish and we have no influence on the British government. The Care office has now closed," she said.
Hassan holds joint Irish, British and Iraqi citizenship.
The group who kidnapped Hassan from outside her Baghdad home two weeks ago has threatened to behead her unless Britain withdraws its troops from Baghdad and the authorities in Iraq free all women held in Iraqi prisons.
Ahern, whose country is militarily neutral and is officially opposed to the US-led presence in Iraq, stressed that Hassan was a particularly inappropriate target.
"Margaret has no political associations. She represents nobody but the vulnerable and the poor," Ahern said. "Your quarrel is not with Margaret. Nor is it with the Irish people, who have been a firm friend of the Arab nations."
Hassan was born in Dublin, then moved with her family to England as a child. She moved to Iraq 32 years ago, married an Iraqi economist, and became an Iraqi citizen in 1980.
She has directed Care International's Baghdad work, overseeing the distribution of medicines and other aid, since the early 1980s.