An elderly Australian woman has been released by an al-Qaeda-linked terror group three weeks after she and her doctor husband were snatched from a village in Burkina Faso where they had been running a medical clinic.

Jocelyn Elliott, 82, appeared at a press conference in the town of Dosso in neighbouring Niger on Saturday alongside Issoufou Mahamadou, the country's president.

Her release came a day after a video purportedly released by al-Qaeda in the Islamic Maghreb (AQIM) emerged in which the group confirmed it was holding the pair and would be releasing Mrs Elliott due to public pressure and because its leaders did not believe in involving women in war.

The Elliotts moved to Burkina Faso in 1972 on a "mission from God" to build a clinic in the small town of Djibo where Dr Elliott, 84, was the sole surgeon, performing up to 150 operations a month. Since their abduction, there have been regular marches by locals calling for their release.

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Dressed in traditional West African dress, Mrs Elliott appeared tired and shaken. She was said by friends to be "embarrassed" by the attention.

"To the Burkina and Niger authorities, I thank you for your efforts," she told the press in halting French.

It remains unclear how Mrs Elliott came to be in Dosso, which is around 400 miles to the east of Djibo.

Initial intelligence reports suggested the couple would be taken to Mali, where Emirate of the Sahara, the AQIM-affiliated group said to have taken them, is based.

Alpha Barry, a Burkinabe foreign affairs spokesman, said that no ransom was paid. "For now, we know that her husband is alive and is doing well," he added. "We will do everything we can to get him out."

The Elliotts' family they were "deeply grateful" for her release and appealed for her husband also to be freed.

AQIM specialises in kidnappings, trafficking arms and drugs and claimed responsibility for an attack on a hotel and cafe in Ougadougou the same day the Elliotts were snatched in which 30 people, mainly foreigners, died.