An Australian woman has been freed after she and her husband were kidnapped by an Al Qaeda-affiliated group in Burkina Faso, Prime Minister Malcolm Turnbull has confirmed.

Key points: Niger's President presented Jocelyn Elliott to journalists at a news conference in Dosso

Niger's President presented Jocelyn Elliott to journalists at a news conference in Dosso Malcolm Turnbull confirmed release and said Julie Bishop spoke with Elliott family in Australia

Malcolm Turnbull confirmed release and said Julie Bishop spoke with Elliott family in Australia Mr Turnbull declined to comment on prospect of Ms Elliott's husband being released

The president of Niger, Mahamadou Issoufou, presented Jocelyn Elliott to journalists at a news conference in Dosso, south-western Niger, and said authorities were intensifying efforts to secure the release of her husband.

The circumstances of her release and how she arrived in Niger were not immediately clear.

Ken and Jocelyn Elliott, who are in their 80s, have lived in Burkina Faso since 1972. ( ABC News )

Mr Turnbull confirmed her release, saying that Foreign Minister Julie Bishop had been speaking with the Elliott family in Australia.

"We want to thank the Government of Niger and the Government of Burkina Faso, which of course is where the Elliotts were living when they were kidnapped," he told the ABC's Insiders program.

"We want to thank them for the work that they're doing, and ... we prefer to say very little about this case publicly other than to say that we obviously continue to cooperate with those Governments and we thank them for their efforts."

Mr Turnbull declined to comment on the prospect of Ms Elliott's husband also being released, only saying the Australian Government would continue to stay in touch with Burkina Faso.

Ms Bishop also confirmed she had spoken to Ms Elliott.

"I spoke to her this morning — she was well, she was relieved, she was very tired," she said.

"Our overriding concern is now for her husband."

The Elliott family also thanked authorities for their assistance, saying in a statement they were "deeply grateful" for the safe release of their mother.

"We are trusting that the moral and guiding principles of those who have released our mother will also be applied to our elderly father who has served the community of Djibo and the Sahel for more than half his lifetime," the statement said.

Militant group Al Qaeda in the Islamic region of Magreb (AQIM) claimed responsibility for the kidnapping in an audio statement on Saturday.

The statement also said the group had decided to release one of the captives — a woman — unconditionally due to public pressure and guidance from Al Qaeda leaders to not involve women in war.

"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.

The couple in their 80s were originally from Perth but had lived in Djibo, near Baraboule, since 1972.

For over 40 years, the pair ran a 120-bed medical clinic in the town before being kidnapped on January 15.

They were abducted from Djibo the same day Al Qaeda fighters raided a restaurant and hotel in Burkina Faso's capital, Ouagadougou, and killed 30 people, many of whom were foreigners.

Reuters