Ministry spokesman Lutfullah Mashal said: "We don't think Jaish-e Muslimeen has control over them. You can tell by the deadlines and the demands which keep being broken and relaxed."
"We think they are being held by some armed robbers who abducted them. Our reports suggest that the hostages are still in or around Kabul," he added.
Annetta Flanigan from Northern Ireland, Kosovan Shqipe Hebibi and Filipino diplomat Angelito Nayan were seized by armed men in central Kabul on 28 October after helping to run presidential elections won by US-backed incumbent Hamid Karzai.
But the Jaish-e Muslimeen group says it holds the three and has called for the release of 26 jailed suspects in return for the hostages.
However, it has gradually relaxed its demands and successive deadlines have passed without apparent incident.
Mulla Sabir Mumin, one of the spokesman for Jaish-e-Muslimeen, said earlier the group's Shura, or Consultative Council, met on Tuesday to discuss the fate of the captives after talks with the government via intermediaries had proven fruitless.
The group has been calling for the release of at least 15 suspects held in Afghan jails.
A government official said authorities were considering offering the group a ransom, but this offer had been rejected.
Mumin said Jaish-e-Muslimeen had become frustrated with talks through intermediaries with the government, and would not continue with them, but it was willing to talk to the United Nations.
The spokesman added that a final decision would, however, be taken by their leader, Akbar Agha, who said he did not favour the notion of the captives being killed.
The UN employees' captors are
calling for a prisoner-swap deal
Mashal said the Jaish-e-Muslimeen might be in contact with the other group whose men in camouflage uniforms snatched the workers from their car.
"We think the gang may have been trying to make contact with groups that were interested in them," he said. "But we don't think that Jaish has control over them - they are just a small group trying to make publicity."
Some diplomats have speculated that the snatching could have been the handiwork of men loyal to a rival of President Karzai, disgruntled by the handling of the 9 October election and its aftermath, and trying to profit from the act.
Mashal said security forces believed Jaish-e Muslimeen bought a video showing the frightened UN workers and a captor with his face hidden by a scarf that appeared on Aljazeera three days after they went missing.
He said leader of Jaish-e-Muslimeen, Agha, did not have the resources to snatch three foreigners in Kabul.
"We are sure they are not far away," he said of the trio. If Jaish-e-Muslimeen were holding them, they would have released another video, he said.
The Afghan government says it
has tight security over Kabul
The captives have not been heard of since the beginning of last week when two were allowed to make calls home.
Mashal said security forces had tight control over routes in and out of Kabul immediately after the captive-taking. "We don't think they have gone out of Kabul province.
"We are keeping our fingers crossed, we are trying our best to find the hostages with intelligence, surveillance and raids."
He also said: "We hope the kidnappers come to realise that it is not just the international community against them, but Afghans as well, and there will be no place for them in Afghanistan or for their families if they don't give up the hostages."