The group, calling itself the Swords of Righteousness Brigade. said the four were spies working undercover as Christian peace activists.
Aljazeera could not verify any of the information on the tape.
The tape, which aired on Tuesday, showed four men and a British passport belonging to Norman Kember.
The British government and the Christian Peacemaker Teams group have both reported that Kember was among four activists taken hostage on Saturday.
A white-haired man, shown in the passport photograph, could be seen sitting on the floor next to three other men in the video.
In the corner of the video were two crossed black swords and the name of the group written in red Arabic script.
The video had a date stamp indicating it was recorded on 27 November.
The captors say the men are
Christian Peacemaker Teams issued a statement on Tuesday confirming that the four men were associated with their organisation.
The group said it had had a team in Iraq since October 2002, working with US and Iraqi detainees and training others in nonviolent intervention and human rights documentation.
Kember and another person were part of a visiting delegation, while two of the group’s staff based in Iraq were also taken, the statement said.
“The team’s work has focused on documenting and focusing public attention on detainee abuses, connecting citizens of Iraq to local and international human rights organisations, and accompanying Iraqi civilians as they interact with multinational military personnel and Iraq’s government officials,” the group said.
The statement said those taken hostage knew the risks when they went into Iraq.
The organisation said it “does not advocate the use of violent force to save our lives should we be kidnapped, held hostage, or caught in the middle of a conflict situation”.
The Canadian government had announced on Sunday that two of four aid workers who were kidnapped in Iraq were Canadian.
An American and a Briton were also reportedly kidnapped.
The British Foreign Office said the matter was under investigation.
The US embassy in Baghdad has only confirmed that one of its citizens had gone missing.