Mujao spokesman Abu Walid Sahraoui, told journalists that the group would post a video of the hostage shortly.
The group which says it is an offshoot of the organisation which calls itself Al-Qaeda in the Islamic Maghreb, has not provided details of its demands in exchange for the hostage.
On Wednesday night the group had said 61-year old Gilberto Rodriguez Leal, who was born in Portugal but is a French citizen, was being held by jihadists, without specifying which armed group had him in their possession.
Mauritania's national news agency ANI reported that Leal was kidnapped on Tuesday night in the town of Diema in the western Kayes region bordering Mauritania and Senegal.
However according to French sources, he was kidnapped in Nioro, further north.
Foreign minister Laurent Fabius said today that the French government had intelligence that Leal was still alive.
"The search is continuing. Mali is in contact with its neighbours, especially Mauritania where the kidnappers could take the hostage before returning him to northern Mali," said a regional security source, who did not wish to be named.
The kidnapping brings to 13 the number of hostages held by hardline Islamists in the region, since a coup in Bamako in March. Seven of these are French.
Islamist groups with links to Al-Qaeda conquered the entire north of Mali, an area the size of France or Texas, in the wake of the coup, and have enforced a brutal form of sharia law.
Western governments, prompted by growing fears the vast arid zone could become a haven for terrorists, are backing regional plans for a military force to intervene in Mali and reclaim control of its north.
France is leading the calls for intervention, but Foreign Minister Laurent Fabius said Thursday it was still a way off.