The vice president of the rebels, known as the National Movement for the Liberation of the Azawad, or NMLA, said the Malian military attacked them first.
"Our men were preparing to garrison themselves at their base in Foita near the border when they were surprised by the Malian military," said Mahamadou Djeri Maiga, the NMLA's vice president, speaking in Ouagadougou, the capital of neighboring Burkina Faso. "We thought they were on patrol. Then early this morning they attacked us with heavy weapons."
"If the army attacks, we will react," he added. "This is a flagrant violation of the accord."
In June, the rebels signed an agreement mediated by the president of Burkina Faso, agreeing to a cease-fire in order to allow Mali's presidential election to go ahead on July 28. The rebels also agreed to garrison their fighters, but the insurgents were frequently spotted outside their assigned bases in the northern province of Kidal.
Talks are to begin later this year between the government of Mali's new leader, President Ibrahim Boubacar Keita, and the NMLA rebels. However, the idea of negotiating with them remains deeply unpopular in southern Mali, as last year's Tuareg uprising marked the beginning of months of turmoil for the sprawling African country.
Helped by al-Qaida's fighters in the region, they swept across northern Mali, seizing a territory the size of France by April 2012. They fell out with their al-Qaida allies in June of last year, and were chased out. Mali's north became a de facto Islamic state until January of this year, when the French forces intervened to help push them out.
While the Islamic extremists have mostly melted into the countryside, the NMLA immediately returned to the province of Kidal, where separatist sentiment remains high.
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Ouedraogo contributed to this report from Ouagadougou, Burkina Faso.