Movement for Oneness and Jihad in West Africa says it is punishing France for intervening in Malian security affairs.
Groups linked to an offshoot of Al-Qaeda in the Islamic Maghreb (AQIM) control large swathes of northern Mali
A Malian group calling itself the Movement for Oneness and Jihad in West Africa (MUJAO) has claimed responsibility for the kidnapping of a French citizen two days ago.
Abu Walid Sahraoui, spokesperson for MUJAO, one of the groups occupying northern Mali, said on Thursday: "We claim responsibility for the kidnapping of the Frenchman in south-western Mali near the Mauritanian border."
The group said it would post a video of the hostage shortly.
Gilberto Rodriguez Leal, 61, was kidnapped on Wednesday and it was reported he was being held by jihadists, without specifying which armed group had him in their possession.
The kidnapping of Leal, who was born in Portugal but holds French citizenship, brings to 13 the total number of people held by force in the West African country. Seven of these are French nationals.
MUJAO, which describes itself as an offshoot of Al-Qaeda in the Islamic Maghreb (AQIM), has not provided details on its demands in exchange for the hostage.
"With God's blessing, the mujahedin are holding a Frenchman, whose country wants to lead armies against the Muslim people," Abdoul Hicham, a top MUJAO leader, told the AFP news agency.
France has been instrumental in drafting a UN Security Council resolution adopted last month which paves the way for the regional bloc ECOWAS to send troops to Mali to try to wrest control of the country's northern region from the fighters.
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. But French sources said he was kidnapped in Nioro, further north.
Regional security sources told AFP that the hunt for Leal and his kidnappers was underway on Thursday.
"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," a security official told AFP on condition of anonymity.
Fighters linked to al-Qaeda took the entire north of Mali, an area the size of France or Texas, in the wake of the March 2012 coup.
They have since enforced a brutal form of sharia law, sparking fears the region could become the Afghanistan of Africa, with fighters carrying out Taliban-stlye attacks beyond Mali's borders.
Western governments, fearing they could become targets of the group, are backing regional plans for a military force to intervene in Mali and reclaim control of its north.
French foreign minister Laurent Fabius said on Thursday more still needed to be done before troops are deployed.
"We are not there yet," he told BMFTV. "Malian forces must first be reconstituted and neighbouring countries must provide elements. This is a matter that is first of all up to the Africans."
He added that the French government had intelligence that the hostage Leal was still alive.