The militant group Al Qaeda in the Islamic region of Magreb (AQIM) has claimed responsibility for the January 15 kidnapping of two Australians in northern Burkina Faso, according to an audio statement.

The statement, released on the group's official Telegram channel, also said the group had decided to release one of the captives — a woman — unconditionally.

"The primary motive behind their kidnapping was an attempt to [gain] release of our captives who sit behind bars and suffer the pain of imprisonment, as well as being deprived of their basic rights," the recording stated.

Dr Ken Elliott and his wife Jocelyn, who are in their 80s, have operated a 120-bed clinic in the town of Djibo for over 40 years.

They were abducted from the town as Al Qaeda fighters raided a restaurant and hotel across the West African nation in the capital Ouagadougou — an attack that left dozens dead, most of them foreigners.

In the recording, AQIM said it was releasing the woman under public pressure and in accordance with what it said was guidance from Al Qaeda leaders not to involve women in war.

A spokesperson for the Department of Foreign Affairs and Trade (DFAT) said the Government was "aware" of the situation.

"We are in close contact with the family in what is a very difficult time, the safety and welfare of Dr and Mrs Elliott are our overriding concern," they said.

"The family has requested privacy and the Government will not be providing further comment at this time."

Reuters/ABC