The armed forces said on social media that the strikes "neutralised several terrorist pick-up trucks" at a military camp evacuated by UN peacekeepers last week in the strategic northern town.
The army appealed to people "not to give in to the terrorists' propaganda intended to tarnish the reputation of the Malian armed forces".
The Permanent Strategic Framework (CSP), an alliance of predominantly Tuareg armed groups, said 14 people had died, including eight children gathered in front of a school.
It said they were killed by Turkish-made drones belonging to Mali's army.
Residents and witnesses, speaking mostly on condition of anonymity out of safety concerns, said between six and nine people died.
"Six people, including children, were killed by air strikes by the Malian army," said one health worker. "In the hospital, we have injured people."
On Saturday, the army said on social media that it had "neutralised" a certain number of targets a day earlier using air power.
The targets were operating inside the camp near Kidal that the UN's stabilisation mission vacated last week, it said.
Tuesday's incident marked the first killings in Kidal since the Tuareg-dominated rebel groups resumed hostilities in August.
Fears of a confrontation in the town -- long a centre of defiance and launching point for independence rebellions -- have been building for some time.
The insubordination of the town and of the Kidal region, where the army suffered humiliating defeats between 2012 and 2014, poses a major sovereignty issue for the junta-led government.
Since seizing power in 2020, Mali's military rulers have made the restoration of sovereignty their mantra.
But Kidal is controlled by the separatist rebel groups.
They launched an insurgency in 2012 and agreed to a ceasefire in 2014 and a peace deal in 2015, before taking up arms again in August.
The independence uprising in 2012 coincided with insurgencies by radical Islamist groups.
Unlike the rebels, the jihadists have never stopped fighting the state, plunging Mali into a political, security and humanitarian crisis that has spread to neighbouring Burkina Faso and Niger.
- Calls to Turkey -
Violence has escalated in the north since August, with the military, rebels and jihadists vying for control as the UN mission evacuates its camps, triggering a race to seize territory.
The rebels do not want the peacekeepers to hand their camps back to the Malian army, saying it would contravene the ceasefire and peace deals struck with the government in 2014 and 2015.
The army on October 2 dispatched a large convoy towards Kidal in anticipation of the UN's departure.
But UN forces, citing the "deteriorating security situation" and threats to its peacekeepers, accelerated their pull-out, upsetting the ruling junta, which wanted the departure to coincide with the army's arrival.
Instead, when the mission left the Kidal camp last week, the rebels immediately seized control.
While the peacekeepers said they had been forced to destroy some of their equipment, they also left some behind.
A local resident who worked for the mission before its pull-out told AFP that some of Tuesday's victims were residents who had gathered in front of the camp to collect equipment.
The CSP alliance of rebel groups said a drone strike had hit a group of children in front of a school near the camp.
The alliance said it was asking Turkey to "review" its policy of selling drones to the junta and to the Russian paramilitary group Wagner, which it says the junta is working with.
Established in 2013, the UN's MINUSMA mission had for the past decade maintained around 15,000 soldiers and police officers in Mali. About 180 members have been killed in hostile acts.
Since July, it has withdrawn nearly 6,000 civilian and uniformed personnel, after the ruling junta demanded the mission depart from Mali.
The deadline for withdrawal, set by the UN Security Council, is December 31.
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