In an exclusive video aired by Aljazeera on Saturday,
the captives appeared blindfolded and surrounded by hooded armed men.
Each man, identified himself then said: "My job consists of installing and furnishing camps at Taji base." Taji, a US base, is 25km north of Baghdad.
The captives wore normal clothes and appeared to be in good health.
The captors described themselves as al-Tawhid and al-Jihad group, which reportedly has links with suspected al-Qaida operative Abu Musab al-Zarqawi.
The US and British embassies in Iraq said earlier they were making their best efforts to get the three captives released.
US nationals Jack Hensley and Eugene "Jack" Armstrong and
British engineer Kenneth Bigley were seized by armed men early on Thursday from their house in Baghdad's affluent al-Mansur district.
All three work for GSCS, a United Arab Emirates-based firm that has won several building contracts in Iraq.
The seizing of the three men was the latest in a string of high-profile abductions of westerners in Iraq.
Two French journalists were abducted almost a month ago while two Italian female aid workers, along with two of their Iraqi colleagues, were seized from their offices on 7 September.