The group threatened in a videotape obtained by Aljazeera to kill the captives if the company failed to cease operations and pull out of Iraq within three days.
Fighters opposed to the US-led military presence in Iraq have regularly targeted contractors working for foreign forces to put pressure on their governments.
Earlier in the day, another Iraqi group threatened to kill two Americans and a British man held captive unless female prisoners in Abu Ghraib and Um Qasr prisons were released within 48 hours.
In an exclusive video aired by Aljazeera on Saturday, the captives appeared blindfolded and surrounded by hooded armed men.
Two Americans and a British man
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 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 doing their best to get the three captives released.
US nationals Jack Hensley and Eugene “Jack” Armstrong along with 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 taken hostage 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.