One of the Australian missionaries kidnapped by an Al Quaeda-affiliated group in Burkina Faso has been released, though her husband remains in captivity.

Jocelyn Elliot was released after Al Qaeda in the Islamic Maghreb (AQIM) announced in a video message it would free her. Her husband, surgeon Dr Ken Elliot, is still being held.

AQIM said it would set her free so as "not to make women involved in the war." Its message said: "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."

She was released in neighbouring Niger.

Their family released a statement saying: "The Elliott family are deeply grateful for the safe release of our mother Jocelyn. 

"We wish to convey our great appreciation to the authorities in ‪#‎Niger‬ and ‪#‎Burkina‬ Faso for their support and assistance in facilitating Mrs Elliott's release.

"For over four decades she has served the Burkinabe people together with our father Dr Ken Elliott. They are separated now but united in their desire to bring healing and hope to the people of Northern Burkina Faso and the surrounding regions.

"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. We respectfully request that they be allowed to continue their work together, providing essential surgical services."

The Elliots have lived in Djibo, near the Malian border, since the 1970s and have built up a 120-bed hospital where Dr Elliott is the only surgeon. They are both in their 80s. They were kidnapped on the day AQIM struck Burkina Faso's capital Ouagadougou in an attack that killed at least 27 people.

Local people have campaigned for Dr Elliott's release. The hospital is the only one for hundreds of kilometres and the campaign's Facebook page pleads for his return, saying his "numerous patients are waiting for him".

"Elliott is all for us and we need him like a baby needs his mother," said resident Moussa Dicko, quoted on the page.

"Elliott is a Burkinabe and a humane person," said Francois Ramde. "He represents the best of humanity."

"Let the name of God not be used in connection with this ignoble act because it was God who sent Elliott to us and will bring him back," said Roots Hassane.