The family of an Australian doctor and his wife abducted in Burkina Faso have urged the kidnappers to release the couple so that they can continue their life-saving charity work in the West African country.

Surgeon Ken Elliott and his wife Jocelyn disappeared from their home on Friday near the northern town of Djibo where they have run a medical center for four decades.

A statement on behalf of their daughter and two sons issued by Australia's Department of Foreign Affairs and Trade on Tuesday said the children had been heartened by an outpouring of support from 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."