Sanda Abou Mohamed, a spokesperson for the group Ansar Dine, said the couple were executed according to sharia law in the town of Aguelhok.
A resident of the nearby city of Kidal, who had spoken to witnesses in Aguelhok, said the couple were buried up to their necks, then pelted with stones until they died. The resident requested anonymity because he feared for his safety.
The West African nation, once seen as a pillar of democracy in the troubled region, has been split in two since a coup in March. Tuareg rebels took control of Mali's vast north but they have since been driven out by al-Qaeda-linked extremists seeking to impose their radical interpretation of sharia law. An estimated 300 000 people have fled.
There was international condemnation after extremist fighters in the ancient city of Timbuktu destroyed centuries-old shrines to Islamic saints revered by Sufi Muslims.
Mali's interim president, Dioncounda Traore, has called for talks with the extremists. In his first national address after a two-month absence – recovering in Paris from injuries sustained when he was beaten by supporters of the coup – Traore said on Sunday he would lead talks to form a unity government and open dialogue with Muslim fundamentalists.
Traore (70) said the country would be led by a high council consisting of himself and two vice-presidents. One of the VPs would be in charge of a committee which would reform the army, as well as deal with the country's northern half.
Engaging armed groups
A committee would also be set up to attempt to negotiate with the north, he said. "This committee will be charged with engaging with the armed groups in the north of Mali, in order to speak of peace … with the aim of finding via dialogue a negotiated political solution to the crisis.
"Given the complexity of this crisis and the extent of the distress of our people from the north … we must together, I say together, clear the path ahead to free our country from these invaders, who only leave desolation, deprivation and pain in their wake."
His comments also come as the president of Côte d'Ivoire, Alassane Ouattara, told a French newspaper that Mali's neighbours would consider military intervention within weeks against the extremists.
In the interview in the French weekly Le Journal du Dimanche, Ouattara, who also leads the body representing West African nations, said: "If the situation does not evolve favourably and rapidly, yes, there will be a military intervention in Mali. It seems inevitable."
He added: "I think we can talk in weeks, not in months. There is urgency." – © Guardian News and Media 2012