France's "crusaders and Zionist Jews will have to pay for its attack on the Muslims of northern Mali," said the spokesman, Hacen Ould Khalil. "I hope France realizes that there will be dozens of Mohammed Merahs and Khaled Kelkal(s)."
Merah, believed to be a French national of Algerian descent, said he was a self-styled al Qaeda-trained jihadist. He was the chief suspect in a series of shootings, including an attack on a Jewish school, in France in 2012. He was killed in a police raid.
Kelkal was of Algerian origin and is believed responsible for a series of attacks on French soil in the 1990s.
The spokesman told the magazine that his group has contacted the French authorities and started negotiations.
"The goal was never to kill or hurt the hostages," he added.
Then he explained what al Qaeda-linked militants in the Sahara want:
The end of the French intervention in Mali; the liberation of Omar Abdel-Rahman, "the blind sheikh" incarcerated in the United States for his role in the 1993 World Trade Center bombings; and the freeing of Aafia Siddiqui, a Pakistani scientist who is incarcerated in the United States on terrorism charges.
France denies any communication with Belmoktar's group, according to the publication.
France sending more troops?
In recent weeks, French President Francois Hollande has said that if his country had not intervened, Mali "probably would have fallen into the hands of terrorists."
Now 3,150 French soldiers have been assigned to the French mission, dubbed Operation Serval. At least 2,150 of them are on Malian territory, the French have said.
The government is considering sending more troops, it said Monday.
The Islamists are well-equipped and well-trained, French officials have said. But advances made by the Malian army toward cities that the Islamists previously controlled "constitutes a certain military success for the Bamako government and for French forces," said French Defense Minister Jean-Yves le Drian.
"I reaffirm my total confidence in our soldiers who are in combat with determination in the mission decided by the French president." he said. "It aims to restore sovereignty to Mali on its territory and to prevent the risk of the constitution of a terrorist sanctuary in the heart of Africa."
Rebel control over Diabaly was one of the chief concerns to Mali and France as they tried to stop the Islamists' movement into the south.
French and Malian forces retook Konna from militants Friday, a French source said. But gunfire could still be heard there on Monday.
As fighting continues, many people are being cut off and are in need of basic supplies.
The U.N. Security Council in December authorized the deployment of an African-led International Support Mission in Mali, and West African leaders met Saturday in Ivory Coast to discuss speeding up deployment of troops.
The regional bloc -- the Economic Community Of West African States -- has said it has 3,300 regional troops on standby.