The video showed the three captives, British-Irish woman Annetta Flanigan, Kosovar woman Shqipe Hebibi and Filipino diplomat Angelito Nayan, seated on the floor in the corner of a room in an unidentified location.
The trio were snatched at gunpoint from their vehicle in Kabul on Thursday by armed men belonging to the group, Jaish-e-Muslimin (Army of Muslims).
They called for the release of Afghan and non-Afghan prisoners held by the Afghan government as well as prisoners at the US military base in Guantanamo Bay, Cuba.
They also called on UN organisations operating in Afghanistan to leave the country.
All three had been contracted by the UN to oversee Afghanistan's first presidential election on 9 October.
At the same time, the captors have reportedly said that the trio would be killed unless all Taliban and al-Qaida prisoners are released from US custody by noon (0730 GMT) on Wednesday.
Mulla Sayyid Muhammad Akbar Agha, leader of the group, said the group had four demands.
"The UN should leave Afghanistan and it should call Britain and America's meddling in Afghanistan illegal," he said.
"Those who have no military involvement in Afghanistan, such as the Philippines, must call Britain and America's meddling in Afghanistan illegal and must stop its contributions through the UN for America and Britain's activities."
"The UN should leave Afghanistan and it should call Britain and America's meddling in Afghanistan illegal"
Sayyid Muhammad Akbar Agha,
He also demanded that Kosovo and Britain immediately withdraw their forces from Afghanistan and that all Muslim prisoners in Afghanistan and Cuba, "be they Taliban or al-Qaida", be freed.
According to an Australian newspaper report, when it was pointed out to Agha that neither Kosovo nor the Philippines have troops in Afghanistan, he replied: "Their countries should condemn the invasion by other countries of Afghanistan."
The kidnappings have stoked fears among the 2000-strong foreign community that groups in Afghanistan may be copying tactics used by anti-US forces in Iraq.
"We call on those holding them not to harm them," United Nations spokesman Manoel de Silva e Almeida told a news briefing on Sunday. "All three require medical attention and the best response to such a situation is their immediate release."