Aljazeera on Thursday aired a video from the group calling itself the Islamic Army in Iraq, showing the men.
The group said the two drivers, employed by a Kuwaiti company, were seized while they were driving their trucks into a US base.
Aljazeera quoted the group as saying the two men would be tried according to Islamic sharia law.
The Islamic Army in Iraq is one of several groups fighting the interim Iraqi government and its US backers and has claimed responsibility for attacks as well as abductions and killings of several captives.
The Polish woman was shown
Meanwhile, another armed group said it had seized a Polish woman working in Iraq and demanded that Poland withdraw its forces from the country to ensure her release.
In a videotape made available to Aljazeera, a woman was shown seated between two masked men, one pointing a gun to her head.
The captive said she had worked in Iraq for a long time. She called for the withdrawal of Polish troops from the country and the release of Iraqi female prisoners from Abu Ghraib prison.
The tape also showed a black banner with the name of the previously unknown group – Abu Bakr al-Siddiq al-Salafyia.