Also Wednesday, a man wearing a belt packed with explosives killed at least 17 Iraqi soldiers and wounded 28 others when he blew himself up inside a restaurant on an Iraqi army base north of Baghdad, army officials said.
The lunchtime explosion took place in Khalis, about 12 miles northwest of Baqouba, Iraqi army Col. Saleh al-Obeidi said. Baqouba is 35 miles northeast of Baghdad.
There were no details available on the operation in Baghdad that led to the release of Douglas Wood, a 64-year-old engineer and resident of California, who was abducted in late April by a militant group calling itself the Shura Council of the Mujahedeen of Iraq.
The Australian government had refused to bend to the kidnappers' demands but immediately sent a team of diplomats, police and military personnel to Baghdad to seek his release.
"Mr. Wood was recovered a short while ago in Baghdad in a military operation that I am told was conducted by Iraqi forces in cooperation in a general way with force elements of the United States," Prime Minister John Howard told Australia's Parliament on Wednesday.
"He's now under the protection of the Australian emergency response team in Baghdad," Howard told parliament. "I understand that he is well, he's undergoing medical checks at the present time."
Iraqi legislators, meanwhile, seemed close to agreement Wednesday on a demand by Sunni Arabs for more participation in the effort to draft a constitution.
Insurgents blew up a pipeline near Baghdad late Tuesday that transports crude between the domestic refineries of Beiji and Doura, a police officer said Wednesday. It was still burning Wednesday, he added.
Police battled with and killed two gunmen in this oil-rich northern city early Wednesday, a day after a suicide bomber killed 23 people and wounded nearly 100 after striking outside a bank as retirees waited to cash their pension checks.
Elsewhere, five Iraqi soldiers were killed and two wounded in a suicide car bombing at a checkpoint in Kan'an, 30 miles north of Baghdad, and the bodies of 24 men -- victims of recent insurgent ambushes in the west of the country -- were transported to a hospital in the capital.
Also Tuesday, two US soldiers were killed in separate attacks in Baghdad while two Marine died in combat operations in western Iraq's volatile Anbar province, the military said.
Kirkuk has become a flashpoint for sectarian tension and Tuesday's violence was the worst to hit the ethnically mixed city, 180 miles north of Baghdad, since the war started in March 2003.
There was more bloodshed in central Kirkuk early Wednesday when police killed two gunmen who fired on their patrol from a speeding car, police Col. Burhan Taha said. A third militant was captured and two police were wounded during the gunfight.
The two American soldiers were killed in Baghdad on the 230th anniversary of the formation of the US Army. One soldier was assigned to the 3rd Infantry Division and was killed in a roadside bomb attack in southern Baghdad. The other was serving with the 18th Military Police Brigade and died in a rocket-propelled grenade blast. Two other soldiers were wounded in that attack.
Two US Marines died as a result of separate roadside bomb blasts in Fallujah, 40 miles west of Baghdad, and near Rutba, a town close to the Jordanian border.
At least 1,708 US military members have died since the war began in 2003, according to an Associated Press count.
Also Tuesday, US Marines and Iraqi soldiers killed five Iraqi civilians at an entrance to the volatile western town of Ramadi, 70 miles west of Baghdad, shortly after a suicide attack on a military checkpoint left one Iraqi soldier dead, the military said.
Separately, two Bulgarian soldiers were killed and another injured late Tuesday when their vehicle slid from a dike into a canal about 35 miles southeast Diwaniya, a city in south-central Iraq where about 400 Bulgarian soldiers are serving.
At least 12 Bulgarian soldiers have died in Iraq. Another three Bulgarians were among 11 civilians killed when a Bulgarian-owned commercial helicopter was shot down April 21 north of Baghdad.
Insurgents have routinely launched deadly attacks in Kirkuk with the apparent aim of creating ethnic tension among the Kurdish, Sunni, Shia and Turkmen population.
The latest bombing coincided with the swearing in of veteran Kurdish guerrilla leader Massoud Barzani as the first president of Iraq's northern Kurdistan region in nearby Irbil, 50 miles north of Kirkuk.
Kurds have long coveted Kirkuk as the capital of an autonomous Kurdish region encompassing all three of their northern provinces.
Saddam forced nearly 100,000 Kurds out of the city as part of an "Arabization" plan. The Shia political parties that control the government have shied away from the issue of giving Kurds control of the city, saying that the central government would retain future control of its oil riches.
Prime Minister Ibrahim al-Jaafari, speaking in parliament after the Kirkuk attack, also accused the insurgents of targeting civilians -- as the number of people killed by militants since the April 28 inception of his Shia-dominated government hit at least 1,018 people, including US forces.
"They are trying now to avoid the military areas, the areas controlled by the multinational or Iraqi forces and they are now conducting their operations in the markets," al-Jaafari told parliament shortly before a vote of confidence.
Al-Jaafari's 37-member government was overwhelmingly approved by a show of hands in the 275-member parliament. But the government has been criticized for its inability to stop insurgent attacks.