The al-Qaeda group says it seized Frenchman Pierre Camatte in Mali
Mali has freed four militants from jail weeks after al-Qaeda's North African branch threatened to kill a French hostage if the men were not released.
The authorities insisted they had not given into al-Qaeda's demands, saying that the four men had served their sentences and were due to be freed.
The release has been criticised by other countries in the region.
The group snatched Frenchman Pierre Camatte from his hotel in Menaka, near the Niger border, on 25 November.
It is thought he is being held in the northern Mali desert by the same group which is holding three Spanish hostages and an Italian couple.
They were kidnapped in neighbouring Mauritania last November.
Al-Qaeda in the Islamic Maghreb issued a statement in early January saying they would kill Mr Camatte if the four members of its group being held by Mali were not freed.
Reports say the four men were sentenced last week to nine months in jail.
They had been in custody since last June, and were freed on the weekend.
The Spanish news agency Efe reported that neighbouring Mauritania expressed alarm at the release, with the ruling party saying it exposed the rest of the region to "enormous risks".
The UK recently warned its nationals not to visit northern Mali because of the threat of attack by the North African branch of al-Qaeda.
The militants were believed to be behind the murder of British hostage Edwin Dyer in June.
Also in June, an American teacher was killed in Mauritania, with the same group later claiming it had killed him for spreading Christianity in the Islamic state.