The men burst into governor Abd al-Karim al-Rawi's house on Wednesday and seized three of his sons after a fierce gun battle with his security personnel, an Aljazeera correspondent reported.
The home was then set ablaze, according to police in the city of Ramadi, 110km west of Baghdad.
Resistance fighters trying to overthrow Iraq's US-installed government have captured scores of foreigners and Iraqis over the past four months.
Most have been released but several have been killed, with at least four foreigners beheaded.
US planes hit
In related news, one resistance fighter was killed and 11 US soldiers were wounded when a military camp outside Ramadi came under gunfire and mortar attack, the US military said on Wednesday.
"The camp around Ramadi came under attack around 1pm (0900 GMT). Ten US service members were injured, one enemy killed and one enemy wounded," a US military spokeswoman said.
Iraqi medical sources also said a local woman was killed during the clashes. Luaya Hamadi died and her husband and three children were hurt when their house was thought to have been hit in the crossfire.
At 2.30pm (1030 GMT), two US aircraft were forced to land after coming under small-arms fire; one pilot was wounded and both planes sustained damage.
The spokeswoman was unable to confirm the type of aircraft hit.