The tape showed the two engineers, identified by relatives as Thomas Nitzschke and Rene Braeunlich, seated on the floor with at least four armed men standing behind them.
The timer shown in the corner of the tape, aired by Al-Jazeera television, indicated it was filmed at 10:08 on Jan. 24, less than two hours after they were abducted in the northern industrial city of Beiji, 155 miles north of Baghdad.
"The (German) government condemns this cruel kidnapping in the strongest possible terms," Chancellor Angela Merkel said after a video of the two men was aired. "We appeal urgently to the perpetrators to release our two compatriots without delay."
The German hostages were seen speaking but Al-Jazeera did not broadcast any audio and the station did not report any demands beyond the hostages calling for German government intervention to secure their release.
A handwritten black banner was shown on the tape reading: "Supporters of Tawhid and Sunnah Brigades," a previously unknown group. Tawhid is the Arabic word for monotheism and Sunnah refers to the teachings of the prophet Muhammad.
In other developments:
A U.S. spokesman says a gun battle broke out at a checkpoint in Kirkuk, 180 miles north of Baghdad, and three men wearing Iraqi police uniforms inside a car were shot dead. American troops captured a fourth man from the car, but found no police identity documents on the men. The military says two U.S. soldiers were killed Saturday in separate roadside bomb blasts.