The tape, obtained on Sunday by Associated Press Television News, shows a man who identifies himself as Douglas Wood, 63, an Australian resident of California and works in Iraq. He is shown seated between two people wearing masks and pointing automatic weapons at him.
On the videotape, the Shura Council of the Mujahidin of Iraq claims responsibility for the abduction.
"Everybody knows the position of the Australian government in relation to hostage demands," Prime Minister John Howard told the Australian Broadcasting Corp radio on Monday.
"We can't have the foreign policy of this country dictated by terrorists."
Wood's wife, Pearl, said she had seen the tape and that the man being held was definitely her husband. She said he had worked in Iraq as an engineer for about a year and a half.
In the tape, Wood said he did not want to die and appealed to US President George Bush, British Prime Minister Tony Blair and Howard to pull their soldiers out of Iraq and leave the country to Iraqis to look after themselves.
Downer said a task force would
try to negotiate Wood's release
Howard said on Monday Australia had established a special task force to try to secure Wood's release, but would not elaborate on what actions it might take. He said under no circumstances would Australia negotiate with "terrorists".
Foreign Minister Alexander Downer said the task force, made up of federal police and officials from the foreign and defence ministries, would head to Iraq as soon as possible to begin working for Wood's release.
Downer said that while refusing to meet demands to withdraw troops, Australia would do all it can to secure the captive's freedom.
Michael McKinley, a security expert at the Australian National University, said the task force would most likely consist of diplomats, special forces, intelligence officers and trained hostage negotiators.
Despite the prime minister's strong remarks, McKinley said Australia would most probably try to open dialogue with the captors and intervene on Wood's behalf.
But he added: "The problem in this case is the demands are absolute."
Australia has about 1370 troops
McKinley said the impact of the captors standoff on Australia's support for the Iraq mission would be mixed.
"I think the long-term effect is for declining support," McKinley said, but he added: "The immediate response could well be that nobody wants to be intimidated, so they will stand fast on the current position."
The video's release came as Australian Defence Minister Robert Hill visited troops in Iraq as well as the country's Prime Minister-designate Ibrahim al-Jafari.
Australia sent 2000 troops to take part in the US-led invasion of Iraq in 2003, and now has about 1370 troops in the region.
So far, one Australian serviceman has been killed on duty in Iraq - Flight Lieutenant Paul Pardoel, who was serving with the British Royal Air Force.
In January, Australian journalist John Martinkus was kidnapped in Baghdad and released unharmed a short time later.