"If they have been kidnapped then we ask that they be released. These people have no military activities and are just ordinary workers looking for jobs abroad," he told Aljazeera.
"We respect all Iraqis and there is no reason to kidnap them [Nepalese] because they went there only to find work."
Nepal has banned its nationals from travelling to or working in Iraq but many Nepalese are known to have gone there from elsewhere in the Middle East.
"We do not have any military presence in Iraq and we do not have official means to manage the travelling of our citizens. They went on their own," added the minister.
Army of Ansar al-Sunna's website showed on Sunday the men holding up their passports in front of a black banner carrying the group's name. It also showed a cropped picture of the hostages together.
The group had earlier announced the capture of the 12 Nepalese on 19-20 August because of their cooperation with US occupation forces in Iraq.
"We are displaying the pictures of the Nepalese prisoners to set an example for anyone who allows himself to fight Islam and Muslims and cooperates with the occupying crusader forces in Iraq," said a statement issued along with the pictures.
It was not immediately possible to verify the authenticity of the pictures.
Cooperating with US
The group said on Friday it had captured the 12 on Thursday and Friday because of their cooperation with US forces in Iraq.
Armed fighters in Iraq have waged a campaign of seizing foreign workers aimed at driving out individuals, companies and troops supporting US forces and the new Iraqi interim administration.
Scores of captives have been taken. Some have been released but at least nine have been killed.