Aljazeera aired a video on Thursday showing three of the men held captive in front of a banner bearing the words al-Jaish al-Islami fi al-Iraq (the Islamic Army in Iraq).
A statement accompanying the footage said they had seized six Iraqis, two Lebanese and two Indonesians.
The group demanded that the captives' company stop all work it is performing for "occupation forces".
It was not immediately clear if the group was a division of the Jaish al-Islami that kidnapped two French journalists because the latest captors further identified themselves as "the western division".
The tape also showed two of the hostages kneeling under a black banner, with masked men holding machine guns above their heads.
The Lebanese employer of the 10 captives has appealed to their abductors to release them.
In a statement, a copy of which was obtained by Aljazeera, Qaswa al-Bawadi Company said its operations in Iraq were confined to the Iraqi private sector and that it had no dealings with the US troops.
Various groups have seized scores of foreigners in Iraq since April. Most of them have been released, but around 30 have been killed.
Meanwhile, a Foreign Ministry official in Beirut, Lebanon, confirmed that two Lebanese had been captured in Iraq.
The official, speaking on condition anonymity, said the Lebanese embassy in Baghdad informed the foreign ministry of the capture.
Later, another official, who also refused to be identified, said
captors in Iraq had released a Lebanese captive identified as Imad Basila and said he was in good health.
But it was not clear if Basila was one of the 10 workers seized. There are at least three other Lebanese still being held captive from separate incidents.