Hassan, held captive in Iraq for nearly a month, was thought to have been killed in a video received by Aljazeera.
However, Aljazeera on Tuesday decided not to broadcast the video as it could not be sure that the woman was Hassan. An Aljazeera official said the channel would also not air it out of respect for the feelings of its audience.
The video showed a masked man using a pistol to shoot a blindfolded woman that may have been Hassan.
The hostage's family, in a statement in London, said she was most likely murdered. The family said she "has probably gone and at last her suffering has ended".
Her Iraqi husband, Tahsin Hassan, said he was aware of the video which appeared to show the killing of his wife.
"The body has not been returned by those who killed her," Howard said before leaving for a meeting of leaders of the Asia Pacific Economic Cooperation forum in Chile.
Tahsin asked his wife's captors to
tell him what they did with her
Earlier in the day Howard had told parliament that a body found in Falluja by the US military on Sunday appeared "to have been Margaret's".
A British embassy official in Baghdad told Reuters it had not been confirmed whether the body was Hassan.
"We are urgently seeking clarification of the identity of the body," the official said.
The British embassy in Baghdad said the tape was probably genuine.
Tahsin Hassan, in a statement broadcast by Britain's Sky News television, said: "The video may be genuine, but I do not know.
"I beg those people who took Margaret to tell me what they have done with her. They can tell. I need her. I need her back to rest in peace," he said.
"Margaret lived with me in Iraq for 30 years. She dedicated her life to serving the Iraqi people. Please, now, please return her to me."
Dublin-born Margaret Hassan was seized on 19 October while on her way to work at Care International, for which she was Iraq country director.
She had appeared in videotapes released by her unknown captors calling on the British government to withdraw its troops from Iraq.
A campaign of kidnappings and killings has gripped Iraq in recent months with more than 35 foreign captives killed.
Some armed groups have used the tactic to try to force US-led troops and foreigners to leave Iraq.
But many abductions have been attributed to criminal gangs taking advantage of lawlessness in the troubled country.