American Kevin King and Australian Timothy Weekes were professors at the American University of Afghanistan in Kabul.

They were abducted in August from their vehicle outside the university by gunmen in security forces uniforms.

Later that month US forces in Afghanistan failed in an attempt to rescue the men, the Pentagon said.

In the video, which purports to have been shot on 1 January and was posted online, the men say they have been kept "in good condition".

But they appeal to US President-elect Donald Trump to offer a prisoner swap for their release, saying they will be killed if he does not negotiate.

The US state department declined to comment on the video or confirm its authenticity, other than to "condemn" hostage-taking.

Australia's foreign ministry said the "Australian government has been working closely with other governments to secure the release of an Australian man kidnapped in Afghanistan in August 2016," but declined to comment further "in the interests of his own safety and well-being".

The American University of Afghanistan said it was saddened by the video, and called for the men to be freed immediately.

In an another development, the US military said an investigation had determined that 33 civilians were killed, and 27 wounded, in a joint US-Afghan military operation in November during which US troops fired on Afghan homes in the province of Kunduz.

"US forces returned fire in self-defence at Taliban who were using civilian houses as firing positions," a US military statement said.

Afghan special forces with US support were targeting Taliban leaders in Boz village, but called in air support when they were fired on from surrounding civilian buildings and began to take casualties, the statement said.

After the operation there were angry protests from civilians, who brought bodies of some of the dead to the governor's office in Kunduz city. A New York Times reporter counted 14 children among the dead. One man said he had lost seven members of his family.