Eight European hostages, including five from France, being held by Al-Qaeda in the Islamic Maghreb (AQIM) are safe, the group has said.
The statement on Saturday from AQIM coincided with rallies across France organised by the families of French hostages who were seized in Niger in September 2010 to mark more than 1,000 days of captivity.
Writing on its Twitter account, AQIM said: "We would like to assure the families and relatives of the hostages that their sons are safe, despite the fact that we have announced before France's intervention in Mali that [such intervention] is like signing the execution orders of the hostages."
The statement accused French President Francois Hollande of "impudence and arrogance", and "executing his own citizens who are apprehended by us", an apparent reference to a French hostage killed in March two years after he was captured in northern Mali.
French newspapers reported this week that the hostages had been transferred to Algeria and were in the hands of AQIM's new chief, Yahia Abou el Hamam. The French government declined to comment on the report.
AQIM said that it had been open to negotiations in the past three years "with clear and reasonable conditions" but that the group were "met with rejection at times, conceit and disregard at others, and provocation by the French government".
The message repeated previous statements by AQIM that it would kill the hostages if there were any new French military interventions in North Africa, but said it remained open to negotiations to free them.
France sent troops to northern Mali in January to help fight armed groups that had siezed control of large swathes of territory and had imposed Islamic law.
The troops began withdrawing in April but a peacekeeping force from West Africa remains in place.
The French government has said it does not negotiate with hostage takers.
Hollande said on a visit to Qatar that "we are always seeking contacts" to have the hostages freed, adding that the situation was "unbearable" for the relatives of the hostages, who have been held for 1,000 days".
AQIM said it would soon release a video of the five French hostages and three other Europeans.
At least eight French citizens, a Swede, a Dutchman, and a British-South African have been kidnapped in recent years in parts of the Sahara desert.
One Frenchman, kidnapped in Nigeria, close to the border with Niger, is believed to be being held by either AQIM or an affiliated group.
Another was kidnapped last year in Mali, near the Mauritanian border, but Saturday's statement did not appear to refer to either of these.
AQIM did confirm in the statement that one French hostage, Philippe Verdon, who was kidnapped in Hombori in northern Mali in November 2011, had been killed in March in response to the French military intervention in the north of Mali.
The hostages referred to in the AQIM statement were previously thought to have been held in northern Mali before the French-led campaign in January drove out the fighters who had seized control of the region after a Tuareg separatist uprising and a military coup in the capital Bamako.
French President Francois Hollande justified the military intervention in Mali partly by saying it would prevent northern Mali being used as a launch pad for attacks in Africa and in the West.