The tape did not show the engineer but included his identification card, listing his name as Joao Jose Vasconcelos, 55.
The tape also showed American and Jordanian cash apparently seized in the kidnapping.
The captors said the ambush was carried out as a joint attack between the Mujahidin Brigades and the Army of Ansar al-Sunna but included no threats or demands. The statement said a Briton and a Brazilian working for a US company were killed.
Iraqi police identified the dead as a Briton working for a London-based security firm and an Iraqi.
The missing Brazilian worked for the Sao Paulo-based Constructora Norberto Odebrecht SA, one of Latin America's biggest construction companies, and was employed at the power station near Baiji.