When French troops seized Kidal's airport a month ago, the MNLA took control of the town itself.
An MNLA spokesman told the BBC its fighters had entered Kidal on Saturday and found no Islamist militants there.
BBC: French troops in Mali take Kidal, last Islamist holdout
The declaration was made in a statement posted online by the secretary general of the Azawad National Liberation Movement (MNLA).
Our correspondent says French forces who entered Kidal found members of the secular National Movement for the Liberation of Azawad (MNLA) there.
BBC: French troops in Mali take Kidal, last Islamist holdout
Many MNLA fighters are said to have fled west into Mauritania rather than get caught up in the showdown between the French and the rebels.
The MNLA is a secular, nationalist movement opposed to al Qaeda.
Maj Traore said the men had apparently gone to join the forces of the MNLA, a Tuareg separatist group which launched a rebellion last year in northern Mali.
BBC: Mali crisis: Relief in Diabaly as French forces roll in
The MNLA, made up of ethnic Tuareg rebels, staged their coup against Mali's central government after returning to Mali well-armed from fighting for late Libyan leader Moammar Gadhafi.
French troops are at the airport in Kidal but rebels from a Tuareg group who want their own homeland in northern Mali - the MNLA - still controls the town itself.
But the alliance quickly collapsed, and the Islamists drove out the Tuareg separatist group - the National Movement Liberation of Azawad (MNLA) - from the main cities and towns in the north.
Ethnic Tuareg rebels of the separatist party MNLA, who had returned to Mali well-armed from fighting for late Libyan leader Moammar Gadhafi, staged a military coup last year against the Malian government.
Almost ignored amid the confusion in Bamako and the fears of Islamists in the north are the MNLA - the separatist Tuareg rebels who launched the initial offensive with reinforcements from post-revolutionary Libya.
The Islamists formed a broad and loose coalition in northern Mali, but only after they had allied with, and then turned against, the Tuareg separatists of National Movement for the Liberation of Azawad (MNLA).
Douentza, 75 miles away, is now in the hands of the MNLA. The famed city of Timbuktu, not so long ago a popular tourist destination for adventurous Europeans, is now ruled by Ansar Dine.
Professor Jeremy Keenan of the School of Oriental and African Studies in London says it's difficult to know how many people the MNLA has under arms and to separate its core force from hangers-on.
Perhaps emboldened by liberation in Tunisia and Libya, in January 2012, the National Liberation Movement of Azawad (MNLA) and Ansar Dine, the most prominent Tuareg armed groups, launched a rebellion that pushed the government from northern Mali.
Late last year Ansar Dine, a jihadist group constituted largely of local Tuareg, even joined the peace talks that the government had already started with the secular Tuareg rebels of the National Movement for the Liberation of Azawad (MNLA).
While the main Tuareg rebel group, the National Movement for the Liberation of Azawad (known by its French acronym, MNLA), did much of the early fighting, Ansar Dine took control of cities such as Timbuktu as government forces fled.
Cheikh Modibo Diarra, the recently ousted transitional prime minister in Mali (and former NASA scientist) said in November that he was open to talks in Burkina Faso with both the MNLA and the jihadists of Ansar Dine on the condition that they were Malian citizens with a purely Malian agenda.
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