The alliance — which includes the Coordination of Azawad Movements, CMA, a coalition of separatist groups dominated by ethnic Tuaregs — also claimed it shot down two planes during the attack Sunday on two military camps.
Its account of events, which took place in the town of Lere in the Timbuktu region, diverged from that of the Malian army.
The army said five soldiers were killed and 11 others were missing. It admitted to having lost a plane, but said it had "neutralized" more than 30 assailants.
In a statement seen on social networks on Wednesday, the rebel groups reported that eight of their fighters had died and 12 were wounded, following three hours of fighting.
They said 35 soldiers were killed and dozens more injured. The pilot of one of the downed fighter jets had died, they added, while the second was not found.
"Six soldiers (were) taken prisoner, some of whom could soon be handed over to independent structures for health reasons," the statement, signed by the Permanent Strategic Framework, CSP, said.
It claimed they had taken "total control of the camps" Sunday before leaving them on Monday.
Information provided by both camps is difficult to verify in the remote area.
Sunday's operation was the latest attack against army positions in northern Mali, which, in addition to suffering frequent jihadist operations, has seen a resurgence of activity by separatist armed groups in recent weeks.
The CMA resumed its operations against the Malian army earlier this month, after months of tensions with the government.
It had signed a peace agreement with the central state in 2015 intended to put an end to hostilities triggered by a 2012 rebel insurrection, which paved the way for armed groups linked to al-Qaida to conquer most of the north.
The insurgencies triggered a military intervention by France and plunged the Sahel into conflict that has left thousands dead.
The jihadists groups have never stopped fighting the Malian state.
In recent weeks, the al-Qaida-affiliated alliance Support Group for Islam and Muslims (GSIM) has claimed several attacks on the army.
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