Malian troops began the offensive to retake the town after clashes over the weekend there, during a visit from Prime Minister Moussa Mara. The failure is regarded as an embarrassment to the Malian government and military.
Kidal is considered emblematic of authority over the surrounding territory, and Malians likely will not believe the government has full control unless Kidal is under government command.
"All of Kidal, including the Malian military camp, the regional governor's office and the (ancient) Kidal fortress are in our control," said Attaye Ag Mohamed of the Tuareg rebel and Islamist militant group, MNLA.
Mohamed added several Malian soldiers had been killed, wounded or captured.
Witnesses said over a dozen dead Malian troops were found in the streets of the town, and rebels were observed patrolling the streets.
The renewed fighting, between northern Islamist forces and the government, threatens to interrupt the peace process in Mali. Western interests are concerned because they regard the rebel threat as upsetting trade and foreign investment throughout northern and western Africa.