Amid the continued violence, more than 60 Iraqi policemen were reported kidnapped as they returned on Sunday from training in Jordan.
Hassan, 59, was seized on her way to work in Baghdad on October 19 by an unknown group of kidnappers.
She was presumed to be the first foreign female hostage to have been murdered in Iraq, and the second British hostage.
CARE Australia, the charity organization that employs Hassan, said it appeared she had been killed, after Al Jazeera television received a video showing a blindfolded woman hostage being shot in the head.
As her family mourned, Britain voiced outrage over the apparent slaying and European Union aid commissioner Paul Nielson warned that it would make it almost impossible for relief work to continue in Iraq.
The Arab League also denounced the apparent murder.
"This is a criminal and terrorist act, rejected and denounced according to any criteria... and inadmissible by every Arab and Muslim whatever the pretext," a spokesman said, adding that the League is "opposed in principle to targeting civilians."
The news of Hassan's suspected killing came during a wave of violence that saw people killed or wounded across Iraq as US-led troops battled insurgents in several Iraqi cities.
In Fallujah, where US-led troops launched a massive assault on November 8 to wrest the city from insurgents, a US Marine officer said on Wednesday that "the battle is over.
"We've still got pockets of fighters, but it's becoming more and more scarce," said Lieutenant Colonel Leonard DiFrancisci, head of civil affairs for the 1st Regimental Combat Team.
But Arabs voiced outrage at the apparent shooting of an unarmed Iraqi by a US Marine in Fallujah, calling for an immediate investigation of this "war crime."
And there are fears of a humanitarian crisis as US troops have prevented a Red Crescent aid convoy from entering Fallujah, a city of some 300,000 civilians in normal times, saying it was too dangerous.
"As far as the return of civilians, it will be at least a week," said DiFrancisci. "That would be a guess."
At least 39 US soldiers have been killed and 275 wounded so far in Operation Dawn, with at least five Iraqi troops and more than 1,200 insurgents also killed, according to the US military.
The military continued its bid to clear rebels from the northern city of Mosul, while at least 23 people were killed in clashes and attacks elsewhere.
Fourteen people were killed, most of them women and children, and 26 wounded in a bomb explosion and clashes in the town of Baiji, north of Baghdad, police said.
In western Iraq more than 60 policemen were seized on Sunday as they returned from training in Jordan, one of only two men who managed to escape the ambush said.
"We were around 65 policemen returning from training in Jordan when around 20 masked gunmen entered our hotel on Sunday morning in Trebil," Leith Naama Al Kaabi said.
"They hooded all the policemen, tied their hands and took them away," he said.
Iraq's security forces are the target of almost daily attacks by insurgents across the war-torn country.
On October 16 nine policemen from the Karbala region were killed, also on their way back from training in Jordan, when their convoy was ambushed in the so-called "death triangle" south of Baghdad.
Barely a week later 49 army recruits and their three civilian drivers were shot dead execution-style northeast of Baghdad.
In Paris French foreign minister Michel Barnier said that two French journalists being held hostage in Iraq for three months have been taken away from war zones and their lives are not in danger.
Christian Chesnot, 37, a freelancer working for Radio France Internationale and Georges Malbrunot, 41, a contributor to the daily Le Figaro, were abducted along with their Syrian driver, Mohammed Al Jundi, on August 20 by a group south of Baghdad calling itself the Islamic Army of Iraq.
On Thursday French President Jacques Chirac began a two-day visit to Britain for an annual Anglo-French summit, with Iraq as a top issue.
On the eve of the visit, Chirac, who led European opposition to the US-led invasion in March 2003, said he is "not at all sure" that the world has become safer since the downfall of Iraqi dictator Saddam Hussein.
British Prime Minister Tony Blair is US President George W. Bush's staunchest ally on Iraq.
In a BBC television interview that aired late on Wednesday Chirac suggested that the violence in Iraq has helped prompt an increase in terrorism.
SYDNEY - The last remaining Australian aid agency in Iraq, World Vision Australia, announced on Friday that it was pulling out following the murders of its head of operations Mohammed Hushiar, who was shot dead by unknown gunmen in a crowded cafe in the northern city of Mosul on September 29, and of Hassan. The agency had been operating in the country for 18 months and had assisted almost 600,000 people - including 400,000 children - by improving schools, hospitals, health clinics, and youth sporting centers.
© 2004 Agence France-Presse