Aljazeera aired video footage on Tuesday showing a man identified as Ronald Schulz, a security adviser for the Iraqi Housing Ministry.
The group said in the tape it captured the adviser and was giving the US military in Iraq 48 hours to release all Iraqi prisoners, otherwise it would kill him.
The group also demanded the US army compensate the people of Anbar governorate for the losses they have suffered from the frequent US attacks on their cities. Both Falluja and Ramadi are in Anbar province and have come under heavy US fire.
Aljazeera aired the footage but could not verify its authenticity.
The grainy video showed a blond, Western-looking man sitting down with his hands tied behind his back. The video carried the logo of the Islamic Army in Iraq. It also showed an American passport and an Arabic identity card bearing the name Ronald Schulz.
Spate of kidnappings
Last year, a group with the same name killed Italian journalist Enzo Baldoni after Rome refused its demand to pull troops from Iraq.
Italian journalist Enzo Baldoni
was killed by the Islamic Army
The kidnapping comes just days after armed men seized four Christian peace activists, two Canadians, a Briton and an American, as well as a German archaeologist and a French engineer in Iraq.
Thousands of civilians have been kidnapped in Iraq since the fall of Saddam Hussein's government, including more than 200 foreigners.
Some foreigners and many more Iraqis have been seized by criminal gangs seeking ransom, but fighters opposed to the US-led invasion have also captured foreign nationals to pressure their governments to withdraw their armies from Iraq.
Many hostages have been released, but about 50 have been killed, some by beheadings broadcast on the internet.