French-led forces took control of Kidal’s airport last week but have not yet secured the town itself.
After Islamist fighters fled, separatist Tuareg fighters took control of the town.
UN, European and African officials are meeting in Brussels to discuss how to finance and organise rebuilding Mali.
One question is how to hold elections, which have been set for 31 July.
The Tuareg rebels did not want Mali’s army, which is with the French forces, to enter Kidal, accusing its soldiers of killing Tuareg civilians in other towns they have recaptured with the help of the French.
The French intervened in January, fearing that Islamist militants who had controlled Mali’s vast north since April 2012, were about to advance on the capital, Bamako.
The French-led forces recaptured the other main town in northern Mali, Timbuktu and Gao, without a fight.
Islamist fighters are believed to have fled into the mountains around Kidal, near the Algerian border, where French forces have been carrying out air strikes against them.