The son of kidnapped missionaries Ken and Jocelyn Elliott has pleaded for their release as the elderly couple's whereabouts remain unknown.

Stephen Elliott and his two siblings grew up in northern Burkina Faso with their parents, who built and ran a hospital in the small northern town of Djibo. He pleaded with the kidnappers for the safe release of Ken and Jocelyn and thanked the Burkinabe people for their support.

"On behalf of our family I wish to express our gratitude for the messages of encouragement we have been receiving from around Australia and abroad during this difficult time," he told The Australian.

"Understandably we are deeply dismayed by this incident and sincerely hope that our parents are being treated kindly wherever they are," Elliott added.

"We have been particularly heartened by the tremendous support of the Burkinabe people who clearly consider Ken and Jocelyn to be one of their own after all these years of providing surgical services to the region. We would urge the Burkinabe people to continue to show patience as they share in our feelings of loss at this time."

"We also want to extend our sympathy to the victims of the recent tragedy in Ouagadougou and to the people of Burkina Faso as they mourn," he said.

The Elliots were abducted following a terrorist attack on Burkina Faso's capital, Ouagadougou, last Friday that killed 28 people and injured 56. 

Locals in Djibo have started a Facebook page to share news and messages of support for the couple, who are in their 80s.

They were abducted from their home next to the 120 bed hospital they had built brick by brick since they arrived in the 1970s. Although no group has claimed responsibility, it is suspected that they were kidnapped by the al-Qaeda-linked Emirate of the Sahara group. 

Dr Ken Elliott was the only surgeon at the hospital and frequently carried out up to 150 operations a month.

"Our ultimate aim is to show the love of God and the goodness and power of Him through medicine," Dr Elliott previously said of his intentions in a YouTube video detailing their work.

The elderly couple had been looking for a replacement to run the hospital but could not find one because, he suggested, qualified doctors wanted to be "where the jobs and the money are".