In an address broadcast on state-owned television, Kabore identified the victims of the abduction, which took place as al Qaeda fighters were attacking a hotel in the capital, as Kenneth and Jocelyn Elliott.
Burkina Faso's security ministry had earlier said the couple were Austrian citizens.
The kidnapping happened in the Baraboule area, the ministry said in a message sent to reporters.
It was not immediately clear whether the abduction was linked to an attack carried out by al Qaeda fighters against a hotel in the country's capital.